Log in

Relevant bibliographies by topics / Torus bundle group / Journal articles

Journal articles on the topic 'Torus bundle group'

To see the other types of publications on this topic, follow the link: Torus bundle group.

Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 48 journal articles for your research on the topic 'Torus bundle group.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Bunke, Ulrich, and Thomas Nikolaus. "T-duality via gerby geometry and reductions." Reviews in Mathematical Physics 27, no. 05 (June 2015): 1550013. http://dx.doi.org/10.1142/s0129055x15500130.

Full text

Abstract:

We consider topological T-duality of torus bundles equipped with [Formula: see text]-gerbes. We show how a geometry on the gerbe determines a reduction of its band to the subsheaf of S1-valued functions which are constant along the torus fibers. We observe that such a reduction is exactly the additional datum needed for the construction of a T-dual pair. We illustrate the theory by working out the example of the canonical lifting gerbe on a compact Lie group which is a torus bundle over the associated flag manifold. It was a recent observation of Daenzer and van Erp [16] that for certain compact Lie groups and a particular choice of the gerbe, the T-dual torus bundle is given by the Langlands dual group.

APA, Harvard, Vancouver, ISO, and other styles

2

GASHI, QËNDRIM R., and TRAVIS SCHEDLER. "NORMALITY AND QUADRATICITY FOR SPECIAL AMPLE LINE BUNDLES ON TORIC VARIETIES ARISING FROM ROOT SYSTEMS." Glasgow Mathematical Journal 55, A (October 2013): 113–34. http://dx.doi.org/10.1017/s0017089513000542.

Full text

Abstract:

AbstractWe prove that special ample line bundles on toric varieties arising from root systems are projectively normal. Here the maximal cones of the fans correspond to the Weyl chambers, and special means that the bundle is torus-equivariant such that the character of the line bundle that corresponds to a maximal Weyl chamber is dominant with respect to that chamber. Moreover, we prove that the associated semi-group rings are quadratic.

APA, Harvard, Vancouver, ISO, and other styles

3

Poddar, Mainak, and Ajay Singh Thakur. "Group actions, non-Kähler complex manifolds and SKT structures." Complex Manifolds 5, no. 1 (February 2, 2018): 9–25. http://dx.doi.org/10.1515/coma-2018-0002.

Full text

Abstract:

AbstractWe give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler) complex structures on tangential frame bundles of complex orbifolds.

APA, Harvard, Vancouver, ISO, and other styles

4

Lee, Min Ho. "Existence of Torus bundles associated to cocycles." Bulletin of the Australian Mathematical Society 73, no. 3 (June 2006): 345–51. http://dx.doi.org/10.1017/s0004972700035383.

Full text

Abstract:

A Kuga fibre variety is a fibre bundle over a locally symmetric space whose fibre is a polarized Abelian variety. We describe a complex torus bundle associated to a 2-cocycle of a discrete group, which may be regarded as a generalized Kuga fibre variety, and prove the existence of such a bundle.

APA, Harvard, Vancouver, ISO, and other styles

5

Florentino, Carlos, and Thomas Ludsteck. "Unipotent Schottky bundles on Riemann surfaces and complex tori." International Journal of Mathematics 25, no. 06 (June 2014): 1450056. http://dx.doi.org/10.1142/s0129167x14500566.

Full text

Abstract:

We study a natural map from representations of a free (respectively, free abelian) group of rank g in GL r(ℂ), to holomorphic vector bundles of degree zero over a compact Riemann surface X of genus g (respectively, complex torus X of dimension g). This map defines what is called a Schottky functor. Our main result is that this functor induces an equivalence between the category of unipotent representations of Schottky groups and the category of unipotent vector bundles on X. We also show that, over a complex torus, any vector or principal bundle with a flat holomorphic connection is Schottky.

APA, Harvard, Vancouver, ISO, and other styles

6

Biswas, Indranil, Arijit Dey, and Mainak Poddar. "A classification of equivariant principal bundles over nonsingular toric varieties." International Journal of Mathematics 27, no. 14 (December 2016): 1650115. http://dx.doi.org/10.1142/s0129167x16501159.

Full text

Abstract:

We classify holomorphic as well as algebraic torus equivariant principal [Formula: see text]-bundles over a nonsingular toric variety [Formula: see text], where [Formula: see text] is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric variety admits a trivialization in equivariant sense. We also obtain some splitting results.

APA, Harvard, Vancouver, ISO, and other styles

7

BISWAS, INDRANIL. "HOLOMORPHIC PRINCIPAL BUNDLES WITH AN ELLIPTIC CURVE AS THE STRUCTURE GROUP." International Journal of Geometric Methods in Modern Physics 05, no. 06 (September 2008): 851–62. http://dx.doi.org/10.1142/s0219887808003004.

Full text

Abstract:

Let Λ ⊂ ℂ be the ℤ-module generated by 1 and [Formula: see text], where τ is a positive real number. Let Z := ℂ/Λ be the corresponding complex torus of dimension one. Our aim here is to give a general construction of holomorphic principal Z-bundles over a complex manifold X. Let θ1 and θ2 be two C∞ real closed two-forms on X such that the Hodge type (0, 2) component of the form [Formula: see text] vanishes, and the elements in H2(X, ℂ) represented by θ1 and θ2 are contained in the image of H2(X, ℤ). For such a pair we construct a holomorphic principal Z-bundle over X. Conversely, given any holomorphic principal Z-bundle EZ over X, we construct a pair of closed differential forms on X of the above type.

APA, Harvard, Vancouver, ISO, and other styles

8

Abe, Yukitaka. "Homogeneous line bundles over a toroidal group." Nagoya Mathematical Journal 116 (December 1989): 17–24. http://dx.doi.org/10.1017/s0027763000001665.

Full text

Abstract:

A connected complex Lie group without non-constant holomorphic functions is called a toroidal group ([5]) or an (H, C)-group ([9]). Let X be an n-dimensional toroidal group. Since a toroidal group is commutative ([5], [9] and [10]), X is isomorphic to the quotient group Cn/Γ by a lattice of Cn. A complex torus is a compact toroidal group. Cousin first studied a non-compact toroidal group ([2]).Let L be a holomorphic line bundle over X. L is said to be homogeneous if is isomorphic to L for all x ε X, where Tx is the translation defined by x ε X. It is well-known that if X is a complex torus, then the following assertions are equivalent:

APA, Harvard, Vancouver, ISO, and other styles

9

Mangum, Brian, and Patrick Shanahan. "Three-Dimensional Representations of Punctured Torus Bundles." Journal of Knot Theory and Its Ramifications 06, no. 06 (December 1997): 817–25. http://dx.doi.org/10.1142/s0218216597000455.

Full text

Abstract:

In this paper, we construct a complex curve of irreducible [Formula: see text] representations of the fundamental group of a once punctured torus bundle over the circle. These representations are different from those obtained by composing representations in [Formula: see text] with the unique irreducible representation of [Formula: see text] in [Formula: see text]. Moreover, infinitely many of these representations are conjugate to SU(3) representations. We conclude the paper with a computation of the curve in the case that the bundle is the figure-eight knot complement, and we show that for infinitely many Dehn surgeries on the figure-eight knot, there is a representation from this curve that descends to a representation of the fundamental group of the surgered manifold.

APA, Harvard, Vancouver, ISO, and other styles

10

LEVINE, MARC. "MOTIVIC EULER CHARACTERISTICS AND WITT-VALUED CHARACTERISTIC CLASSES." Nagoya Mathematical Journal 236 (March 22, 2019): 251–310. http://dx.doi.org/10.1017/nmj.2019.6.

Full text

Abstract:

This paper examines Euler characteristics and characteristic classes in the motivic setting. We establish a motivic version of the Becker–Gottlieb transfer, generalizing a construction of Hoyois. Making calculations of the Euler characteristic of the scheme of maximal tori in a reductive group, we prove a generalized splitting principle for the reduction from $\operatorname{GL}_{n}$ or $\operatorname{SL}_{n}$ to the normalizer of a maximal torus (in characteristic zero). Ananyevskiy’s splitting principle reduces questions about characteristic classes of vector bundles in $\operatorname{SL}$-oriented, $\unicode[STIX]{x1D702}$-invertible theories to the case of rank two bundles. We refine the torus-normalizer splitting principle for $\operatorname{SL}_{2}$ to help compute the characteristic classes in Witt cohomology of symmetric powers of a rank two bundle, and then generalize this to develop a general calculus of characteristic classes with values in Witt cohomology.

APA, Harvard, Vancouver, ISO, and other styles

11

Biswas, Indranil. "Yang–Mills connections on compact complex tori." Journal of Topology and Analysis 07, no. 02 (March 26, 2015): 293–307. http://dx.doi.org/10.1142/s1793525315500107.

Full text

Abstract:

Let G be a connected reductive complex affine algebraic group and K ⊂ G a maximal compact subgroup. Let M be a compact complex torus equipped with a flat Kähler structure and (EG, θ) a polystable Higgs G-bundle on M. Take any C∞ reduction of structure group EK ⊂ EG to the subgroup K that solves the Yang–Mills equation for (EG, θ). We prove that the principal G-bundle EG is polystable and the above reduction EK solves the Einstein–Hermitian equation for EG. We also prove that for a semistable (respectively, polystable) Higgs G-bundle (EG, θ) on a compact connected Calabi–Yau manifold, the underlying principal G-bundle EG is semistable (respectively, polystable).

APA, Harvard, Vancouver, ISO, and other styles

12

Nayek, Arpita, and S. K. Pattanayak. "Torus quotient of Richardson varieties in orthogonal and symplectic grassmannians." Journal of Algebra and Its Applications 19, no. 10 (October 11, 2019): 2050186. http://dx.doi.org/10.1142/s0219498820501868.

Full text

Abstract:

For any simple, simply connected algebraic group [Formula: see text] of type [Formula: see text] and [Formula: see text] and for any maximal parabolic subgroup [Formula: see text] of [Formula: see text], we provide a criterion for a Richardson variety in [Formula: see text] to admit semistable points for the action of a maximal torus [Formula: see text] with respect to an ample line bundle on [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

13

Fegan, H. D. "Homogeneous bundles and the trace of the heat kernel." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 40, no. 1 (February 1986): 71–82. http://dx.doi.org/10.1017/s1446788700026501.

Full text

Abstract:

AbstractWe study the heat equation on a homogeneous bundle over a compact Lie group. The trace of the heat kernel is explicitly calculated. By comparing this with the formula constructed form the eigenvalues (with multiplicities) of the Laplacian we obtain and unusual formula involving the Clebsch-Gordan numbers. The main method is to use invariance under conjugation to pass from the group to its maximal torus, where a direct calculation can be carried out.

APA, Harvard, Vancouver, ISO, and other styles

14

FROLOV, S. A. "GAUGE-INVARIANT HAMILTONIAN FORMULATION OF LATTICE YANG-MILLS THEORY AND THE HEISENBERG DOUBLE." Modern Physics Letters A 10, no. 34 (November 10, 1995): 2619–31. http://dx.doi.org/10.1142/s0217732395002751.

Full text

Abstract:

It is known that to get the usual Hamiltonian formulation of lattice Yang-Mills theory in the temporal gauge A0=0 one should place on each link a cotangent bundle of a Lie group. The cotangent bundle may be considered as a limiting case of a so-called Heisenberg double of a Lie group which is one of the basic objects in the theory of Lie-Poisson and quantum groups. It is shown in the paper that there is a generalization of the usual Hamiltonian formulation to the case of the Heisenberg double. The physical phase space of the (1+1)-dimensional γ-deformed Yang-Mills model is proved to be equivalent to the moduli space of flat connections on a two-dimensional torus.

APA, Harvard, Vancouver, ISO, and other styles

15

Biswas, Indranil, Krishna Hanumanthu, and D. S. Nagaraj. "Positivity of vector bundles on homogeneous varieties." International Journal of Mathematics 31, no. 12 (September 24, 2020): 2050097. http://dx.doi.org/10.1142/s0129167x20500974.

Full text

Abstract:

We study the following question: Given a vector bundle on a projective variety [Formula: see text] such that the restriction of [Formula: see text] to every closed curve [Formula: see text] is ample, under what conditions [Formula: see text] is ample? We first consider the case of an abelian variety [Formula: see text]. If [Formula: see text] is a line bundle on [Formula: see text], then we answer the question in the affirmative. When [Formula: see text] is of higher rank, we show that the answer is affirmative under some conditions on [Formula: see text]. We then study the case of [Formula: see text], where [Formula: see text] is a reductive complex affine algebraic group, and [Formula: see text] is a parabolic subgroup of [Formula: see text]. In this case, we show that the answer to our question is affirmative if [Formula: see text] is [Formula: see text]-equivariant, where [Formula: see text] is a fixed maximal torus. Finally, we compute the Seshadri constant for such vector bundles defined on [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

16

Huang, Hong. "Kähler–Ricci flow on homogeneous toric bundles." International Journal of Mathematics 31, no. 03 (February 18, 2020): 2050022. http://dx.doi.org/10.1142/s0129167x20500226.

Full text

Abstract:

Assume that [Formula: see text] is a homogeneous toric bundle of the form [Formula: see text] and is Fano, where [Formula: see text] is a compact semisimple Lie group with complexification [Formula: see text], [Formula: see text] a parabolic subgroup of [Formula: see text], [Formula: see text] is a surjective homomorphism from [Formula: see text] to the algebraic torus [Formula: see text], and [Formula: see text] is a compact toric manifold of complex dimension [Formula: see text]. In this note, we show that the normalized Kähler–Ricci flow on [Formula: see text] with a [Formula: see text]-invariant initial Kähler form in [Formula: see text] converges, modulo the algebraic torus action, to a Kähler–Ricci soliton. This extends a previous work of Zhu. As a consequence, we recover a result of Podestà–Spiro.

APA, Harvard, Vancouver, ISO, and other styles

17

Bregman, Corey. "Rational Growth and Almost Convexity of Higher-Dimensional Torus Bundles." International Mathematics Research Notices 2019, no. 13 (October 12, 2017): 4004–46. http://dx.doi.org/10.1093/imrn/rnx243.

Full text

Abstract:

AbstractGiven a matrix $A\in SL(N,\mathbb{Z})$, form the semidirect product $G=\mathbb{Z}^N\rtimes_A \mathbb{Z}$ where the $\mathbb{Z}$-factor acts on $\mathbb{Z}^N$ by $A$. Such a $G$ arises naturally as the fundamental group of an $N$-dimensional torus bundle which fibers over the circle. In this article, we prove that if $A$ has distinct eigenvalues not lying on the unit circle, then there exists a finite index subgroup $H\leq G$ possessing rational growth series for some generating set. In contrast, we show that if $A$ has at least one eigenvalue not lying on the unit circle, then $G$ is not almost convex for any generating set.

APA, Harvard, Vancouver, ISO, and other styles

18

BYTSENKO, ANDREI A., LUCIANO VANZO, and SERGIO ZERBINI. "MASSLESS SCALAR CASIMIR EFFECT IN A CLASS OF HYPERBOLIC KALUZA-KLEIN SPACE-TIMES." Modern Physics Letters A 07, no. 05 (February 20, 1992): 397–409. http://dx.doi.org/10.1142/s0217732392000343.

Full text

Abstract:

In the framework of heat-kernel approach to zeta-function regularization we calculate the one-loop effective potential (Casimir effect) massless scalar field on Kaluza-Klein space-time of the form RD−n×Hn/Γ(2≤n<D). In addition the Selberg trace formula associated with discrete torsion-free group Γ of the n-dimensional Lobachevsky space Hn is used. A negative Casimir effect related to trivial line bundle with character χ=1 is found. A comparison of the results obtained and Casimir effect for massless field on torus backgrounds is also presented.

APA, Harvard, Vancouver, ISO, and other styles

19

Gonçalves, Daciberg Lima, and Sérgio Tadao Martins. "The cohomology ring of the sapphires that admit the Sol geometry." International Journal of Algebra and Computation 28, no. 03 (May 2018): 365–80. http://dx.doi.org/10.1142/s0218196718500170.

Full text

Abstract:

Let [Formula: see text] be the fundamental group of a sapphire that admits the Sol geometry and is not a torus bundle. We determine a finite free resolution of [Formula: see text] over [Formula: see text] and calculate a partial diagonal approximation for this resolution. We also compute the cohomology rings [Formula: see text] for [Formula: see text] and [Formula: see text] for an odd prime [Formula: see text], and indicate how to compute the groups [Formula: see text] and the multiplicative structure given by the cup product for any system of coefficients [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

20

Heil, Wolfgang, and Wilbur Whitten. "The Seifert Fiber Space Conjecture and Torus Theorem for Nonorientable 3-Manifolds." Canadian Mathematical Bulletin 37, no. 4 (December 1, 1994): 482–89. http://dx.doi.org/10.4153/cmb-1994-070-7.

Full text

Abstract:

AbstractThe Seifert-fiber-space conjecture for nonorientable 3-manifolds states that if M denotes a compact, irreducible, nonorientable 3-manifold that is not a fake P2 x S1, if π1M is infinite and does not contain Z2 * Z2 as a subgroup, and if π1M does however contain a nontrivial, cyclic, normal subgroup, then M is a Seifert bundle. In this paper, we construct all compact, irreducible, nonorientable 3-manifolds (that do not contain a fake P2 × I) each of whose fundamental group contains Z2 * Z2 and an infinité cyclic, normal subgroup; none of these manifolds admits a Seifert fibration, but they satisfy Thurston's Geometrization Conjecture. We then reformulate the statement of the (nonorientable) SFS-conjecture and obtain a torus theorem for nonorientable manifolds.

APA, Harvard, Vancouver, ISO, and other styles

21

HOU, BO-YU, DAN-TAO PENG, KANG-JIE SHI, and RUI-HONG YUE. "SOLITONS ON NONCOMMUTATIVE TORUS AS ELLIPTIC CALOGERO–GAUDIN MODELS, BRANES AND LAUGHLIN WAVE FUNCTIONS." International Journal of Modern Physics A 18, no. 14 (June 10, 2003): 2477–500. http://dx.doi.org/10.1142/s0217751x03014228.

Full text

Abstract:

For the noncommutative torus [Formula: see text], in the case of the noncommutative parameter [Formula: see text], we construct the basis of Hilbert space ℋn in terms of θ functions of the positions zi of n solitons. The wrapping around the torus generates the algebra [Formula: see text], which is the Zn × Zn Heisenberg group on θ functions. We find the generators g of a local elliptic su (n), which transform covariantly by the global gauge transformation of [Formula: see text]. By acting on ℋn we establish the isomorphism of [Formula: see text] and g. We embed this g into the L-matrix of the elliptic Gaudin and Calogero–Moser models to give the dynamics. The moment map of this twisted cotangent [Formula: see text] bundle is matched to the D-equation with the Fayet–Illiopoulos source term, so the dynamics of the noncommutative solitons become that of the brane. The geometric configuration (k, u) of the spectral curve det |L(u) - k| = 0 describes the brane configuration, with the dynamical variables zi of the noncommutative solitons as the moduli T⊗ n/Sn. Furthermore, in the noncommutative Chern–Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is identified also with the moment map equation of the noncommutative [Formula: see text] cotangent bundle with marked points. The eigenfunction of the Gaudin differential L-operators as the Laughlin wave function is solved by Bethe ansatz.

APA, Harvard, Vancouver, ISO, and other styles

22

Biswas, Indranil, Ananyo Dan, Arjun Paul, and Arideep Saha. "Logarithmic connections on principal bundles over a Riemann surface." International Journal of Mathematics 28, no. 12 (November 2017): 1750088. http://dx.doi.org/10.1142/s0129167x17500884.

Full text

Abstract:

Let [Formula: see text] be a holomorphic principal [Formula: see text]-bundle on a compact connected Riemann surface [Formula: see text], where [Formula: see text] is a connected reductive complex affine algebraic group. Fix a finite subset [Formula: see text], and for each [Formula: see text] fix [Formula: see text]. Let [Formula: see text] be a maximal torus in the group of all holomorphic automorphisms of [Formula: see text]. We give a necessary and sufficient condition for the existence of a [Formula: see text]-invariant logarithmic connection on [Formula: see text] singular over [Formula: see text] such that the residue over each [Formula: see text] is [Formula: see text]. We also give a necessary and sufficient condition for the existence of a logarithmic connection on [Formula: see text] singular over [Formula: see text] such that the residue over each [Formula: see text] is [Formula: see text], under the assumption that each [Formula: see text] is [Formula: see text]-rigid.

APA, Harvard, Vancouver, ISO, and other styles

23

FORSYTH, IAIN, and ADAM RENNIE. "FACTORISATION OF EQUIVARIANT SPECTRAL TRIPLES IN UNBOUNDED -THEORY." Journal of the Australian Mathematical Society 107, no. 02 (December 21, 2018): 145–80. http://dx.doi.org/10.1017/s1446788718000423.

Full text

Abstract:

We provide sufficient conditions to factorise an equivariant spectral triple as a Kasparov product of unbounded classes constructed from the group action on the algebra and from the fixed point spectral triple. We show that if factorisation occurs, then the equivariant index of the spectral triple vanishes. Our results are for the action of compact abelian Lie groups, and we demonstrate them with examples from manifolds and $\unicode[STIX]{x1D703}$ -deformations. In particular, we show that equivariant Dirac-type spectral triples on the total space of a torus principal bundle always factorise. Combining this with our index result yields a special case of the Atiyah–Hirzebruch theorem. We also present an example that shows what goes wrong in the absence of our sufficient conditions (and how we get around it for this example).

APA, Harvard, Vancouver, ISO, and other styles

24

Morifuji, Takayuki, and Masaaki Suzuki. "Representations of the Braid Group and Punctured Torus Bundles." Kyungpook mathematical journal 49, no. 1 (March 31, 2009): 7–14. http://dx.doi.org/10.5666/kmj.2009.49.1.007.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

de Jesus Nery, Genildo. "Profinite genus of fundamental groups of torus bundles." Communications in Algebra 48, no. 4 (November 26, 2019): 1567–76. http://dx.doi.org/10.1080/00927872.2019.1691573.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

KOSCHORKE, ULRICH. "FIXED POINTS AND COINCIDENCES IN TORUS BUNDLES." Journal of Topology and Analysis 03, no. 02 (June 2011): 177–212. http://dx.doi.org/10.1142/s1793525311000519.

Full text

Abstract:

Minimum numbers of fixed points or of coincidence components (realized by maps in given homotopy classes) are the principal objects of study in topological fixed point and coincidence theory. In this paper, we investigate fiberwise analoga and present a general approach e.g. to the question when two maps can be deformed until they are coincidence free. Our method involves normal bordism theory, a certain pathspace EB and a natural generalization of Nielsen numbers. As an illustration we determine the minimum numbers for all maps between torus bundles of arbitrary (possibly different) dimensions over spheres and, in particular, over the unit circle. Our results are based on a careful analysis of the geometry of generic coincidence manifolds. They also allow a simple algebraic description in terms of the Reidemeister invariant (a certain selfmap of an abelian group) and its orbit behavior (e.g. the number of odd order orbits which capture certain nonorientability phenomena). We carry out several explicit sample computations, e.g. for fixed points in (S1)2-bundles. In particular, we obtain existence criteria for fixed point free fiberwise maps.

APA, Harvard, Vancouver, ISO, and other styles

27

Jakobsen, Mads S., and Franz Luef. "Sampling and periodization of generators of Heisenberg modules." International Journal of Mathematics 30, no. 10 (September 2019): 1950051. http://dx.doi.org/10.1142/s0129167x19500514.

Full text

Abstract:

This paper considers generators of Heisenberg modules in the case of twisted group [Formula: see text]-algebras of closed subgroups of locally compact abelian (LCA) groups and how the restriction and/or periodization of these generators yield generators for other Heisenberg modules. Since generators of Heisenberg modules are exactly the generators of (multi-window) Gabor frames, our methods are going to be from Gabor analysis. In the latter setting, the procedure of restriction and periodization of generators is well known. Our results extend this established part of Gabor analysis to the general setting of LCA groups. We give several concrete examples where we demonstrate some of the consequences of our results. Finally, we show that vector bundles over an irrational noncommutative torus may be approximated by vector bundles for finite-dimensional matrix algebras that converge to the irrational noncommutative torus with respect to the module norm of the generators, where the matrix algebras converge in the quantum Gromov–Hausdorff distance to the irrational noncommutative torus.

APA, Harvard, Vancouver, ISO, and other styles

28

Bismut, Jean-Michel, and John Lott. "Torus bundles and the group cohomology of ${\rm GL}(N,\bold Z)$." Journal of Differential Geometry 47, no. 2 (1997): 196–236. http://dx.doi.org/10.4310/jdg/1214460111.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Adem, Alejandro, F. R. Cohen, and José Manuel Gómez. "Commuting elements in central products of special unitary groups." Proceedings of the Edinburgh Mathematical Society 56, no. 1 (October 24, 2012): 1–12. http://dx.doi.org/10.1017/s0013091512000144.

Full text

Abstract:

AbstractWe study the space of commuting elements in the central product Gm,p of m copies of the special unitary group SU(p), where p is a prime number. In particular, a computation for the number of path-connected components of these spaces is given and the geometry of the moduli space Rep(ℤn, Gm,p) of isomorphism classes of flat connections on principal Gm,p-bundles over the n-torus is completely described for all values of n, m and p.

APA, Harvard, Vancouver, ISO, and other styles

30

Bridson, M. R., and Ch Pittet. "Isoperimetric inequalities for the fundamental groups of torus bundles over the circle." Geometriae Dedicata 49, no. 2 (February 1994): 203–19. http://dx.doi.org/10.1007/bf01610621.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Lee, Min Ho, and Dong Youp Suh. "Torus Bundles over Locally Symmetric Varieties Associated to Cocycles of Discrete Groups." Monatshefte f�r Mathematik 130, no. 2 (June 29, 2000): 127–41. http://dx.doi.org/10.1007/s006050070042.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Tralle, Aleksy. "On Formality of Some Homogeneous Spaces." Symmetry 11, no. 8 (August 5, 2019): 1011. http://dx.doi.org/10.3390/sym11081011.

Full text

Abstract:

Let G / H be a homogeneous space of a compact simple classical Lie group G. Assume that the maximal torus T H of H is conjugate to a torus T β whose Lie algebra t β is the kernel of the maximal root β of the root system of the complexified Lie algebra g c . We prove that such homogeneous space is formal. As an application, we give a short direct proof of the formality property of compact homogeneous 3-Sasakian spaces of classical type. This is a complement to the work of Fernández, Muñoz, and Sanchez which contains a full analysis of the formality property of S O ( 3 ) -bundles over the Wolf spaces and the proof of the formality property of homogeneous 3-Sasakian manifolds as a corollary.

APA, Harvard, Vancouver, ISO, and other styles

33

Lee, Min Ho. "Theta functions on Hermitian symmetric domains and fock representations." Journal of the Australian Mathematical Society 74, no. 2 (April 2003): 201–34. http://dx.doi.org/10.1017/s1446788700003256.

Full text

Abstract:

AbstractOne way of realizing representations of the Heisenberg group is by using Fock representations, whose representation spaces are Hilbert spaces of functions on complex vector space with inner products associated to points on a Siegel upper half space. We generalize such Fock representations using inner products associated to points on a Hermitian symmetric domain that is mapped into a Seigel upper half space by an equivariant holomorphic map. The representations of the Heisenberg group are then given by an automorphy factor associated to a Kuga fiber variety. We introduce theta functions associated to an equivariant holomorphic map and study connections between such generalized theta functions and Fock representations described above. Furthermore, we discuss Jacobi forms on Hermitian symmetric domains in connection with twisted torus bundles over symmetric spaces.

APA, Harvard, Vancouver, ISO, and other styles

34

BROWN, RICHARD J. "Anosov mapping class actions on the $SU(2)$-representation variety of a punctured torus." Ergodic Theory and Dynamical Systems 18, no. 3 (June 1998): 539–54. http://dx.doi.org/10.1017/s0143385798108258.

Full text

Abstract:

Recently, Goldman [2] proved that the mapping class group of a compact surface $S$, ${\it MCG}(S)$, acts ergodically on each symplectic stratum of the Poisson moduli space of flat $ S(2)$-bundles over $S$, $X(S, S(2))$. We show that this property does not extend to that of cyclic subgroups of ${\it MCG}(S)$, for $S$ a punctured torus. The symplectic leaves of $X(T^2-pt., SU(2))$ are topologically copies of the 2-sphere $S^2$, and we view mapping class actions as a continuous family of discrete Hamiltonian dynamical systems on $S^2$. These deformations limit to finite rotations on the degenerate leaf corresponding to $-{\rm Id}$. boundary holonomy. Standard KAM techniques establish that the action is not ergodic on the leaves in a neighborhood of this degenerate leaf.

APA, Harvard, Vancouver, ISO, and other styles

35

Mathai, Varghese, and Jonathan Rosenberg. "$T$-duality for torus bundles with $H$-fluxes via noncommutative topology. {II}. The high-dimensional case and the $T$-duality group." Advances in Theoretical and Mathematical Physics 10, no. 1 (2006): 123–58. http://dx.doi.org/10.4310/atmp.2006.v10.n1.a5.

Full text

APA, Harvard, Vancouver, ISO, and other styles

36

MÜLLER, STEFAN, and PETER SPAETH. "Helicity of vector fields preserving a regular contact form and topologically conjugate smooth dynamical systems." Ergodic Theory and Dynamical Systems 33, no. 5 (June 29, 2012): 1550–83. http://dx.doi.org/10.1017/s0143385712000387.

Full text

Abstract:

AbstractWe compute the helicity of a vector field preserving a regular contact form on a closed three-dimensional manifold, and improve results of Gambaudo and Ghys [Enlacements asymptotiques. Topology 36(6) (1997), 1355–1379] relating the helicity of the suspension of a surface isotopy to the Calabi invariant of the isotopy. Based on these results, we provide positive answers to two questions posed by Arnold in [The asymptotic Hopf invariant and its applications. Selecta Math. Soviet. 5(4) (1986), 327–345]. In the presence of a regular contact form that is also preserved, the helicity extends to an invariant of an isotopy of volume-preserving homeomorphisms, and is invariant under conjugation by volume-preserving homeomorphisms. A similar statement also holds for suspensions of surface isotopies and surface diffeomorphisms. This requires the techniques of topological Hamiltonian and contact dynamics developed by Banyaga and Spaeth [On the uniqueness of generating Hamiltonians for topological strictly contact isotopies.Preprint, 2012], Buhovsky and Seyfaddini [Uniqueness of generating Hamiltonians for continuous Hamiltonian flows. J. Symplectic Geom. to appear, arXiv:1003.2612v2], Müller [The group of Hamiltonian homeomorphisms in the$L^\infty $-norm. J. Korean Math. Soc.45(6) (2008), 1769–1784], Müller and Oh [The group of Hamiltonian homeomorphisms and$C^0$-symplectic topology. J. Symplectic Geom. 5(2) (2007), 167–219], Müller and Spaeth [Topological contact dynamics I: symplectization and applications of the energy-capacity inequality.Preprint, 2011, arXiv:1110.6705v2] and Viterbo [On the uniqueness of generating Hamiltonian for continuous limits of Hamiltonians flows. Int. Math. Res. Not. (2006), 34028; Erratum,Int. Math. Res. Not.(2006), 38748]. Moreover, we generalize an example of Furstenberg [Strict ergodicity and transformation of the torus. Amer. J. Math. 83(1961), 573–601] on topologically conjugate but not$C^1$-conjugate area-preserving diffeomorphisms of the two-torus to trivial$T^2$-bundles, and construct examples of Hamiltonian and contact vector fields that are topologically conjugate but not$C^1$-conjugate. Higher-dimensional helicities are considered briefly at the end of the paper.

APA, Harvard, Vancouver, ISO, and other styles

37

ABE, Yukitaka. "A PROOF OF THE STRUCTURE THEOREM OF COHOMOLOGY GROUPS OF HOLOMORPHIC LINE BUNDLES OVER A COMPLEX TORUS WITHOUT USE OF THE SERRE DUALITY." Memoirs of the Faculty of Science, Kyushu University. Series A, Mathematics 45, no. 2 (1991): 143–54. http://dx.doi.org/10.2206/kyushumfs.45.143.

Full text

APA, Harvard, Vancouver, ISO, and other styles

38

Asselmeyer-Maluga, Torsten. "Braids, 3-Manifolds, Elementary Particles: Number Theory and Symmetry in Particle Physics." Symmetry 11, no. 10 (October 15, 2019): 1298. http://dx.doi.org/10.3390/sym11101298.

Full text

Abstract:

In this paper, we will describe a topological model for elementary particles based on 3-manifolds. Here, we will use Thurston’s geometrization theorem to get a simple picture: fermions as hyperbolic knot complements (a complement C ( K ) = S 3 \ ( K × D 2 ) of a knot K carrying a hyperbolic geometry) and bosons as torus bundles. In particular, hyperbolic 3-manifolds have a close connection to number theory (Bloch group, algebraic K-theory, quaternionic trace fields), which will be used in the description of fermions. Here, we choose the description of 3-manifolds by branched covers. Every 3-manifold can be described by a 3-fold branched cover of S 3 branched along a knot. In case of knot complements, one will obtain a 3-fold branched cover of the 3-disk D 3 branched along a 3-braid or 3-braids describing fermions. The whole approach will uncover new symmetries as induced by quantum and discrete groups. Using the Drinfeld–Turaev quantization, we will also construct a quantization so that quantum states correspond to knots. Particle properties like the electric charge must be expressed by topology, and we will obtain the right spectrum of possible values. Finally, we will get a connection to recent models of Furey, Stoica and Gresnigt using octonionic and quaternionic algebras with relations to 3-braids (Bilson–Thompson model).

APA, Harvard, Vancouver, ISO, and other styles

39

Choi, Seongjun, Meng-Che “Turbo” Ho, and Mark Pengitore. "Rational growth in Torus bundle groups of odd trace." Proceedings of the Edinburgh Mathematical Society, December 6, 2022, 1–53. http://dx.doi.org/10.1017/s0013091522000505.

Full text

Abstract:

Abstract A group is said to have rational growth with respect to a generating set if the growth series is a rational function. It was shown by Parry that certain torus bundle groups of even trace exhibits rational growth. We generalize this result to a class of torus bundle groups with odd trace.

APA, Harvard, Vancouver, ISO, and other styles

40

Zielenkiewicz, Magdalena. "Integration over homogeneous spaces for classical Lie groups using iterated residues at infinity." Open Mathematics 12, no. 4 (January 1, 2014). http://dx.doi.org/10.2478/s11533-013-0372-z.

Full text

Abstract:

AbstractUsing the Berline-Vergne integration formula for equivariant cohomology for torus actions, we prove that integrals over Grassmannians (classical, Lagrangian or orthogonal ones) of characteristic classes of the tautological bundle can be expressed as iterated residues at infinity of some holomorphic functions of several variables. The results obtained for these cases can be expressed as special cases of one formula involving the Weyl group action on the characters of the natural representation of the torus.

APA, Harvard, Vancouver, ISO, and other styles

41

del Moral, M. P. Garcia, C. Las Heras, P. Leon, J. M. Pena, and A. Restuccia. "Fluxes, twisted tori, monodromy and U(1) supermembranes." Journal of High Energy Physics 2020, no. 9 (September 2020). http://dx.doi.org/10.1007/jhep09(2020)097.

Full text

Abstract:

Abstract We show that the D = 11 supermembrane theory (M2-brane) compactified on a M9× T2 target space, with constant fluxes C± naturally incorporates the geometrical structure of a twisted torus. We extend the M2-brane theory to a formulation on a twisted torus bundle. It is consistently fibered over the world volume of the M2-brane. It can also be interpreted as a torus bundle with a nontrivial U(1) connection associated to the fluxes. The structure group G is the area preserving diffeomorphisms. The torus bundle is defined in terms of the monodromy associated to the isotopy classes of symplectomorphisms with π0(G) = SL(2, Z), and classified by the coinvariants of the subgroups of SL(2, Z). The spectrum of the theory is purely discrete since the constant flux induces a central charge on the supersymmetric algebra and a modification on the Hamiltonian which renders the spectrum discrete with finite multiplicity. The theory is invariant under symplectomorphisms connected and non connected to the identity, a result relevant to guarantee the U-dual invariance of the theory. The Hamiltonian of the theory exhibits interesting new U(1) gauge and global symmetries on the worldvolume induced by the symplectomorphim transformations. We construct explicitly the supersymmetric algebra with nontrivial central charges. We show that the zero modes decouple from the nonzero ones. The nonzero mode algebra corresponds to a massive superalgebra that preserves either 1/2 or 1/4 of the original supersymmetry depending on the state considered.

APA, Harvard, Vancouver, ISO, and other styles

42

Galasso, Andrea. "Equivariant fixed point formulae and Toeplitz operators under Hamiltonian torus actions and remarks on equivariant asymptotic expansions." International Journal of Mathematics 33, no. 02 (January 15, 2022). http://dx.doi.org/10.1142/s0129167x22500112.

Full text

Abstract:

Suppose given a holomorphic and Hamiltonian action of a compact torus on a polarized Hodge manifold. Assume that the action lifts to the quantizing line bundle, so that there is an induced unitary representation of the torus on the associated Hardy space which decomposes into isotypes. The main result of this paper is the description of asymptotics along rays in weight space of traces of equivariant Toeplitz operators composed with quantomorphisms for the torus action. The main ingredient in the proof is the micro-local analysis of the equivariant Szegő kernels. As a particular case we obtain a simple approach for asymptotics of the Lefschetz fixed point formula and traces of Toeplitz operators in the setting of ladder representations. We also consider equivariant asymptotic when the decomposition given by the standard circle action is taken into account, in this case one can recall previous results of X. Ma and W. Zhang or of R. Paoletti. We address some explicit computations for the action of the special unitary group of dimension two.

APA, Harvard, Vancouver, ISO, and other styles

43

Bonelli, G., N. Fasola, and A. Tanzini. "Defects, nested instantons and comet-shaped quivers." Letters in Mathematical Physics 111, no. 2 (March 11, 2021). http://dx.doi.org/10.1007/s11005-021-01366-5.

Full text

Abstract:

AbstractWe introduce and study a surface defect in four-dimensional gauge theories supporting nested instantons with respect to the parabolic reduction of the gauge group at the defect. This is engineered from a $$\mathrm{{D3/D7}}$$ D 3 / D 7 -branes system on a non-compact Calabi–Yau threefold X. For $$X=T^2\times T^*{{\mathcal {C}}}_{g,k}$$ X = T 2 × T ∗ C g , k , the product of a two torus $$T^2$$ T 2 times the cotangent bundle over a Riemann surface $${{\mathcal {C}}}_{g,k}$$ C g , k with marked points, we propose an effective theory in the limit of small volume of $${\mathcal C}_{g,k}$$ C g , k given as a comet-shaped quiver gauge theory on $$T^2$$ T 2 , the tail of the comet being made of a flag quiver for each marked point and the head describing the degrees of freedom due to the genus g. Mathematically, we obtain for a single $$\mathrm{{D7}}$$ D 7 -brane conjectural explicit formulae for the virtual equivariant elliptic genus of a certain bundle over the moduli space of the nested Hilbert scheme of points on the affine plane. A connection with elliptic cohomology of character varieties and an elliptic version of modified Macdonald polynomials naturally arises.

APA, Harvard, Vancouver, ISO, and other styles

44

Parry, Walter. "Examples of growth series of torus bundle groups." Journal of Group Theory 10, no. 2 (January 20, 2007). http://dx.doi.org/10.1515/jgt.2007.020.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Webb, Rachel. "The Abelian–Nonabelian Correspondence for I-Functions." International Mathematics Research Notices, November 20, 2021. http://dx.doi.org/10.1093/imrn/rnab305.

Full text

Abstract:

Abstract We prove the abelian–nonabelian correspondence for quasimap $I$-functions. That is, if $Z$ is an affine l.c.i. variety with an action by a complex reductive group $G$, we prove an explicit formula relating the quasimap $I$-functions of the geometric invariant theory quotients $Z\mathord{/\mkern -6mu/}_{\theta } G$ and $Z\mathord{/\mkern -6mu/}_{\theta } T$ where $T$ is a maximal torus of $G$. We apply the formula to compute the $J$-functions of some Grassmannian bundles on Grassmannian varieties and Calabi–Yau hypersurfaces in them.

APA, Harvard, Vancouver, ISO, and other styles

46

Ghazouani, S., and K. Khanin. "The symplectic structure for renormalization of circle diffeomorphisms with breaks." Communications in Contemporary Mathematics, March 19, 2021, 2150016. http://dx.doi.org/10.1142/s0219199721500164.

Full text

Abstract:

The main goal of this paper is to reveal the symplectic structure related to renormalization of circle maps with breaks. We first show that iterated renormalizations of [Formula: see text] circle diffeomorphisms with [Formula: see text] breaks, [Formula: see text], with given size of breaks, converge to an invariant family of piecewise Möbius maps, of dimension [Formula: see text]. We prove that this invariant family identifies with a relative character variety [Formula: see text] where [Formula: see text] is a [Formula: see text]-holed torus, and that the renormalization operator identifies with a sub-action of the mapping class group [Formula: see text]. This action allows us to introduce the symplectic form which is preserved by renormalization. The invariant symplectic form is related to the symplectic form described by Guruprasad et al. [Group systems, groupoids, and moduli spaces of parabolic bundles, Duke Math. J. 89(2) (1997) 377–412], and goes back to the earlier work by Goldman [The symplectic nature of fundamental groups of surfaces, Adv. Math. 54(2) (1984) 200–225]. To the best of our knowledge the connection between renormalization in the nonlinear setting and symplectic dynamics had not been brought to light yet.

APA, Harvard, Vancouver, ISO, and other styles

47

D’Alesio, Stefano. "Derived representation schemes and Nakajima quiver varieties." Selecta Mathematica 28, no. 1 (December 22, 2021). http://dx.doi.org/10.1007/s00029-021-00724-4.

Full text

Abstract:

AbstractWe introduce a derived representation scheme associated with a quiver, which may be thought of as a derived version of a Nakajima variety. We exhibit an explicit model for the derived representation scheme as a Koszul complex and by doing so we show that it has vanishing higher homology if and only if the moment map defining the corresponding Nakajima variety is flat. In this case we prove a comparison theorem relating isotypical components of the representation scheme to equivariant K-theoretic classes of tautological bundles on the Nakajima variety. As a corollary of this result we obtain some integral formulas present in the mathematical and physical literature since a few years, such as the formula for Nekrasov partition function for the moduli space of framed instantons on $$S^4$$ S 4 . On the technical side we extend the theory of relative derived representation schemes by introducing derived partial character schemes associated with reductive subgroups of the general linear group and constructing an equivariant version of the derived representation functor for algebras with a rational action of an algebraic torus.

APA, Harvard, Vancouver, ISO, and other styles

48

Jöricke, Burglind. "Riemann surfaces of second kind and effective finiteness theorems." Mathematische Zeitschrift, June 13, 2022. http://dx.doi.org/10.1007/s00209-022-03018-3.

Full text

Abstract:

AbstractThe Geometric Shafarevich Conjecture and the Theorem of de Franchis state the finiteness of the number of certain holomorphic objects on closed or punctured Riemann surfaces. The analog of these kind of theorems for Riemann surfaces of second kind is an estimate of the number of irreducible holomorphic objects up to homotopy (or isotopy, respectively). This analog can be interpreted as a quantitatve statement on the limitation for Gromov’s Oka principle. For any finite open Riemann surface X (maybe, of second kind) we give an effective upper bound for the number of irreducible holomorphic mappings up to homotopy from X to the twice punctured complex plane, and an effective upper bound for the number of irreducible holomorphic torus bundles up to isotopy on such a Riemann surface. The bound depends on a conformal invariant of the Riemann surface. If $$X_{\sigma }$$ X σ is the $$\sigma $$ σ -neighbourhood of a skeleton of an open Riemann surface with finitely generated fundamental group, then the number of irreducible holomorphic mappings up to homotopy from $$X_{\sigma }$$ X σ to the twice punctured complex plane grows exponentially in $$\frac{1}{\sigma }$$ 1 σ .

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!