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Journal articles on the topic 'Symplectic bundles'

Author: Grafiati

Published: 14 March 2023

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1

Choe, Insong, and George H. Hitching. "Non-defectivity of Grassmannian bundles over a curve." International Journal of Mathematics 27, no. 07 (2016): 1640002. http://dx.doi.org/10.1142/s0129167x16400024.

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Let [Formula: see text] be the Grassmann bundle of two-planes associated to a general bundle [Formula: see text] over a curve [Formula: see text]. We prove that an embedding of [Formula: see text] by a certain twist of the relative Plücker map is not secant defective. This yields a new and more geometric proof of the Hirschowitz-type bound on the isotropic Segre invariant for maximal isotropic sub-bundles of orthogonal bundles over [Formula: see text], analogous to those given for vector bundles and symplectic bundles in [I. Choe and G. H. Hitching, Secant varieties and Hirschowitz bound on ve

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2

Choe, Insong, and G. H. Hitching. "A stratification on the moduli spaces of symplectic and orthogonal bundles over a curve." International Journal of Mathematics 25, no. 05 (2014): 1450047. http://dx.doi.org/10.1142/s0129167x14500475.

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A symplectic or orthogonal bundle V of rank 2n over a curve has an invariant t(V) which measures the maximal degree of its isotropic subbundles of rank n. This invariant t defines stratifications on moduli spaces of symplectic and orthogonal bundles. We study this stratification by relating it to another one given by secant varieties in certain extension spaces. We give a sharp upper bound on t(V), which generalizes the classical Nagata bound for ruled surfaces and the Hirschowitz bound for vector bundles, and study the structure of the stratifications on the moduli spaces. In particular, we c

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3

Benedetti, Gabriele, and Alexander F. Ritter. "Invariance of symplectic cohomology and twisted cotangent bundles over surfaces." International Journal of Mathematics 31, no. 09 (2020): 2050070. http://dx.doi.org/10.1142/s0129167x20500706.

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We prove that symplectic cohomology for open convex symplectic manifolds is invariant when the symplectic form undergoes deformations which may be nonexact and noncompactly supported, provided one uses the correct local system of coefficients in Floer theory. As a sample application beyond the Liouville setup, we describe in detail the symplectic cohomology for disc bundles in the twisted cotangent bundle of surfaces, and we deduce existence results for periodic magnetic geodesics on surfaces. In particular, we show the existence of geometrically distinct orbits by exploiting properties of the

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4

CHOE, INSONG, and GEORGE H. HITCHING. "Lagrangian subbundles of symplectic bundles over a curve." Mathematical Proceedings of the Cambridge Philosophical Society 153, no. 2 (2012): 193–214. http://dx.doi.org/10.1017/s0305004112000096.

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AbstractA symplectic bundle over an algebraic curve has a natural invariantsLagdetermined by the maximal degree of its Lagrangian subbundles. This can be viewed as a generalization of the classical Segre invariants of a vector bundle. We give a sharp upper bound onsLagwhich is analogous to the Hirschowitz bound on the classical Segre invariants. Furthermore, we study the stratifications induced bysLagon moduli spaces of symplectic bundles, and get a full picture for the case of rank four.

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5

Bakuradze, M. "On the Buchstaber Subring in MSp∗." gmj 5, no. 5 (1998): 401–14. http://dx.doi.org/10.1515/gmj.1998.401.

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Abstract A formula is given to calculate the last n number of symplectic characteristic classes of the tensor product of the vector Spin(3)- and Sp(n)-bundles through its first 2n number of characteristic classes and through characteristic classes of Sp(n)-bundle. An application of this formula is given in symplectic cobordisms and in rings of symplectic cobordisms of generalized quaternion groups.

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6

HITCHING, GEORGE H. "RANK FOUR SYMPLECTIC BUNDLES WITHOUT THETA DIVISORS OVER A CURVE OF GENUS TWO." International Journal of Mathematics 19, no. 04 (2008): 387–420. http://dx.doi.org/10.1142/s0129167x08004716.

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The moduli space [Formula: see text] of rank four semistable symplectic vector bundles over a curve X of genus two is an irreducible projective variety of dimension ten. Its Picard group is generated by the determinantal line bundle Ξ. The base locus of the linear system |Ξ| consists of precisely those bundles without theta divisors, that is, admitting nonzero maps from every line bundle of degree -1 over X. We show that this base locus consists of six distinct points, which are in canonical bijection with the Weierstrass points of the curve. We relate our construction of these bundles to anot

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7

de Araujo, Artur. "Generalized quivers, orthogonal and symplectic representations, and Hitchin–Kobayashi correspondences." International Journal of Mathematics 30, no. 03 (2019): 1850085. http://dx.doi.org/10.1142/s0129167x18500854.

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We review the theory of quiver bundles over a Kähler manifold, and then introduce the concept of generalized quiver bundles for an arbitrary reductive group [Formula: see text]. We first study the case when [Formula: see text] or [Formula: see text], interpreting them as orthogonal (respectively symplectic) bundle representations of the symmetric quivers introduced by Derksen–Weyman. We also study supermixed quivers, which simultaneously involve both orthogonal and symplectic symmetries. In particular, we completely characterize the polystable forms of such representations. Finally, we discuss

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8

BISWAS, INDRANIL, та SARBESWAR PAL. "ON MODULI SPACE OF HIGGS Gp(2n, ℂ)-BUNDLES OVER A RIEMANN SURFACE". International Journal of Geometric Methods in Modern Physics 07, № 02 (2010): 311–22. http://dx.doi.org/10.1142/s0219887810004002.

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Let X be a compact connected Riemann surface; the holomorphic cotangent bundle of X will be denoted by KX. Let [Formula: see text] denote the moduli space of semistable Higgs Gp (2n, ℂ)-bundles over X of fixed topological type. The complex variety [Formula: see text] has a natural holomorphic symplectic structure. On the other hand, for any ℓ ≥ 1, the Liouville symplectic from on the total space of KX defines a holomorphic symplectic structure on the Hilbert scheme Hilb ℓ(KX) parametrizing the zero-dimensional subschemes of KX. We relate the symplectic form on Hilb ℓ(KX) with the symplectic fo

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9

BISWAS, INDRANIL, TOMAS L. GÓMEZ, and VICENTE MUÑOZ. "AUTOMORPHISMS OF MODULI SPACES OF SYMPLECTIC BUNDLES." International Journal of Mathematics 23, no. 05 (2012): 1250052. http://dx.doi.org/10.1142/s0129167x12500528.

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Let X be an irreducible smooth complex projective curve of genus g ≥ 4. Fix a line bundle L on X. Let MSp(L) be the moduli space of semistable symplectic bundles (E, φ : E ⊗ E → L) on X, with the symplectic form taking values in L. We show that the automorphism group of MSp(L) is generated by the automorphisms of the form E ↦ E ⊗ M, where [Formula: see text], together with the automorphisms induced by automorphisms of X.

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10

Otiman, Alexandra. "Locally conformally symplectic bundles." Journal of Symplectic Geometry 16, no. 5 (2018): 1377–408. http://dx.doi.org/10.4310/jsg.2018.v16.n5.a5.

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11

BISWAS, INDRANIL, and TOMÁS L. GÓMEZ. "HECKE CORRESPONDENCE FOR SYMPLECTIC BUNDLES WITH APPLICATION TO THE PICARD BUNDLES." International Journal of Mathematics 17, no. 01 (2006): 45–63. http://dx.doi.org/10.1142/s0129167x06003357.

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We construct a Hecke correspondence for a moduli space of symplectic vector bundles over a curve. As an application we prove the following. Let X be a complex smooth projective curve of genus g(X) > 2 and L a line bundle over X. Let [Formula: see text] be the moduli space parametrizing stable pairs of the form (E,φ), where E is a vector bundle of rank 2n over X and φ : E ⊗ E → L a skew-symmetric nondegenerate bilinear form on the fibers of E. If deg (E) ≥ 4n(g(X)-1), then there is a projectivized Picard bundle on [Formula: see text], which is a projective bundle whose fiber over any point [

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12

Ginzburg, Viktor L., and Jeongmin Shon. "On the filtered symplectic homology of prequantization bundles." International Journal of Mathematics 29, no. 11 (2018): 1850071. http://dx.doi.org/10.1142/s0129167x18500714.

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We study Reeb dynamics on prequantization circle bundles and the filtered (equivariant) symplectic homology of prequantization line bundles, aka negative line bundles, with symplectically aspherical base. We define (equivariant) symplectic capacities, obtain an upper bound on their growth, prove uniform instability of the filtered symplectic homology and touch upon the question of stable displacement. We also introduce a new algebraic structure on the positive (equivariant) symplectic homology capturing the free homotopy class of a closed Reeb orbit — the linking number filtration — and use it

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13

Bunk, Severin. "Gerbes in Geometry, Field Theory, and Quantisation." Complex Manifolds 8, no. 1 (2021): 150–82. http://dx.doi.org/10.1515/coma-2020-0112.

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Abstract This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbes with connection and their morphisms, and explain the classification of bundle gerbes with connection in terms of differential cohomology. We then survey how the surface holonomy of bundle gerbes combines with their transgression line bundles to yield a smooth bordism-type field theory. Finally, we exhibit the use of bundle gerbes in geometric quantisation of 2-plectic as well as 1- and 2-shifted s

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14

Hsieh, Po-Hsun. "Symplectic Geometry of Vector Bundle Maps of Tangent Bundles." Rocky Mountain Journal of Mathematics 31, no. 3 (2001): 987–1001. http://dx.doi.org/10.1216/rmjm/1020171675.

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15

Lalonde, François, and Dusa McDuff. "Symplectic structures on fiber bundles." Topology 42, no. 2 (2003): 309–47. http://dx.doi.org/10.1016/s0040-9383(01)00020-9.

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16

Biswas, Indranil, Souradeep Majumder, and Michael Lennox Wong. "Orthogonal and symplectic parabolic bundles." Journal of Geometry and Physics 61, no. 8 (2011): 1462–75. http://dx.doi.org/10.1016/j.geomphys.2011.03.009.

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17

Ojanguren, M., R. Parimala, and R. Sridharan. "Symplectic bundles over affine surfaces." Commentarii Mathematici Helvetici 61, no. 1 (1986): 491–500. http://dx.doi.org/10.1007/bf02621929.

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18

Choe, Insong, and George H. Hitching. "Maximal isotropic subbundles of orthogonal bundles of odd rank over a curve." International Journal of Mathematics 26, no. 13 (2015): 1550106. http://dx.doi.org/10.1142/s0129167x15501062.

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An orthogonal bundle over a curve has an isotropic Segre invariant determined by the maximal degree of a maximal isotropic subbundle. This invariant and the induced stratifications on moduli spaces of orthogonal bundles were studied for bundles of even rank in [I. Choe and G. H. Hitching, A stratification on the moduli space of symplectic and orthogonal bundles over a curve, Internat. J. Math. 25(5) (2014), Article ID: 1450047, 27pp.]. In this paper, we obtain analogous results for bundles of odd rank. We compute the sharp upper bound on the isotropic Segre invariant. Also we show the irreduci

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19

CRASMAREANU, MIRCEA. "DIRAC STRUCTURES FROM LIE INTEGRABILITY." International Journal of Geometric Methods in Modern Physics 09, no. 04 (2012): 1220005. http://dx.doi.org/10.1142/s0219887812200058.

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We prove that a pair (F = vector sub-bundle of TM, its annihilator) yields an almost Dirac structure which is Dirac if and only if F is Lie integrable. Then a flat Ehresmann connection on a fiber bundle ξ yields two complementary, but not orthogonally, Dirac structures on the total space M of ξ. These Dirac structures are also Lagrangian sub-bundles with respect to the natural almost symplectic structure of the big tangent bundle of M. The tangent bundle in Riemannian geometry is discussed as particular case and the 3-dimensional Heisenberg space is illustrated as example. More generally, we s

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20

Schnitzer, Jonas, and Luca Vitagliano. "The Local Structure of Generalized Contact Bundles." International Mathematics Research Notices 2020, no. 20 (2019): 6871–925. http://dx.doi.org/10.1093/imrn/rnz009.

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Abstract Generalized contact bundles are odd-dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local splitting theorem similar to those appearing in Poisson geometry. In particular, in a neighborhood of a regular point, a generalized contact bundle is either the product of a contact and a complex manifold or the product of a symplectic manifold and a manifold equipped with an integrable complex structure on the gauge algebroid of the trivial line

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21

Vinberg, E. "Equivariant Symplectic Geometry of Cotangent Bundles." Moscow Mathematical Journal 1, no. 2 (2001): 287–99. http://dx.doi.org/10.17323/1609-4514-2001-1-2-287-299.

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22

Ebner, Oliver, and Stefan Haller. "Harmonic cohomology of symplectic fiber bundles." Proceedings of the American Mathematical Society 139, no. 08 (2011): 2927. http://dx.doi.org/10.1090/s0002-9939-2010-10707-4.

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23

Bowden, Jonathan. "The topology of symplectic circle bundles." Transactions of the American Mathematical Society 361, no. 10 (2009): 5457. http://dx.doi.org/10.1090/s0002-9947-09-04721-7.

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24

Gotay, Mark J. "On symplectic submanifolds of cotangent bundles." Letters in Mathematical Physics 29, no. 4 (1993): 271–79. http://dx.doi.org/10.1007/bf00750961.

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25

Chantraine, Baptiste, and Emmy Murphy. "Conformal symplectic geometry of cotangent bundles." Journal of Symplectic Geometry 17, no. 3 (2019): 639–61. http://dx.doi.org/10.4310/jsg.2019.v17.n3.a2.

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26

Panin, I., and C. Walter. "Quaternionic Grassmannians and Borel classes in algebraic geometry." St. Petersburg Mathematical Journal 33, no. 1 (2021): 97–140. http://dx.doi.org/10.1090/spmj/1692.

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The quaternionic Grassmannian H Gr ⁡ ( r , n ) \operatorname {H Gr}(r,n) is the affine open subscheme of the usual Grassmannian parametrizing those 2 r 2r -dimensional subspaces of a 2 n 2n -dimensional symplectic vector space on which the symplectic form is nondegenerate. In particular, we have HP n = H Gr ⁡ ( 1 , n + 1 ) \operatorname {HP}^n = \operatorname {H Gr}(1,n+1) . For a symplectically oriented cohomology theory A A , including oriented theories but also the Hermitian K \operatorname {K} -theory, Witt groups, and algebraic symplectic cobordism, we have A ( HP n ) = A ( pt ) [ p ] / (

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27

VAISMAN, IZU. "COUPLING POISSON AND JACOBI STRUCTURES ON FOLIATED MANIFOLDS." International Journal of Geometric Methods in Modern Physics 01, no. 05 (2004): 607–37. http://dx.doi.org/10.1142/s0219887804000307.

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Let M be a differentiable manifold endowed with a foliation ℱ. A Poisson structure P on M is ℱ-coupling if ♯P(ann(Tℱ)) is a normal bundle of the foliation. This notion extends Sternberg's coupling symplectic form of a particle in a Yang–Mills field [11]. In the present paper we extend Vorobiev's theory of coupling Poisson structures [16] from fiber bundles to foliated manifolds and give simpler proofs of Vorobiev's existence and equivalence theorems of coupling Poisson structures on duals of kernels of transitive Lie algebroids over symplectic manifolds. We then discuss the extension of the co

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28

Kurek, J., and W. M. Mikulski. "Symplectic structures on the tangent bundles of symplectic and cosymplectic manifolds." Annales Polonici Mathematici 82, no. 3 (2003): 273–85. http://dx.doi.org/10.4064/ap82-3-8.

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29

Bates, Larry M. "Examples for obstructions to action-angle coordinates." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 110, no. 1-2 (1988): 27–30. http://dx.doi.org/10.1017/s0308210500024823.

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SynopsisWe give examples of symplectic manifolds which are also non-trivial principal torus-bundles with Lagrangian fibres. These bundles are examples of spaces with an obstruction to the global existence of action-angle variables.

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30

Tikhomirov, A. S., S. A. Tikhomirov, and D. A. Vasiliev. "Construction of stable rank 2 bundles on P3 via symplectic bundles." Sibirskii matematicheskii zhurnal 60, no. 2 (2018): 441–60. http://dx.doi.org/10.33048/smzh.2019.60.215.

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31

Tikhomirov, A. S., S. A. Tikhomirov та D. A. Vassiliev. "Construction of Stable Rank 2 Bundles on ℙ3 Via Symplectic Bundles". Siberian Mathematical Journal 60, № 2 (2019): 343–58. http://dx.doi.org/10.1134/s0037446619020150.

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32

BISWAS, INDRANIL, and AVIJIT MUKHERJEE. "QUANTIZATION OF A MODULI SPACE OF PARABOLIC HIGGS BUNDLES." International Journal of Mathematics 15, no. 09 (2004): 907–17. http://dx.doi.org/10.1142/s0129167x04002594.

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Let [Formula: see text] be a moduli space of stable parabolic Higgs bundles of rank two over a Riemann surface X. It is a smooth variety defined over [Formula: see text] equipped with a holomorphic symplectic form. Fix a projective structure [Formula: see text] on X. Using [Formula: see text], we construct a quantization of a certain Zariski open dense subset of the symplectic variety [Formula: see text].

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33

Kobayashi, Shoshichi. "Simple vector bundles over symplectic Kähler manifolds." Proceedings of the Japan Academy, Series A, Mathematical Sciences 62, no. 1 (1986): 21–24. http://dx.doi.org/10.3792/pjaa.62.21.

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34

Timashev, D. "Equivariant Symplectic Geometry of Cotangent Bundles, II." Moscow Mathematical Journal 6, no. 2 (2006): 389–404. http://dx.doi.org/10.17323/1609-4514-2006-6-2-389-404.

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35

Lacirasella, Ignazio, Juan Carlos Marrero, and Edith Padrón. "Reduction of symplectic principal $\mathbb R$-bundles." Journal of Physics A: Mathematical and Theoretical 45, no. 32 (2012): 325202. http://dx.doi.org/10.1088/1751-8113/45/32/325202.

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36

Ding, Fan, and Youlin Li. "Strong symplectic fillability of contact torus bundles." Geometriae Dedicata 195, no. 1 (2017): 403–15. http://dx.doi.org/10.1007/s10711-017-0299-9.

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37

Biswas, Indranil, and Tomás L. Gómez. "Stability of symplectic and orthogonal Poincaré bundles." Journal of Geometry and Physics 76 (February 2014): 97–106. http://dx.doi.org/10.1016/j.geomphys.2013.10.014.

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38

Maley, F. Miller, Jean Mastrangeli, and Lisa Traynor. "Symplectic Packings in Cotangent Bundles of Tori." Experimental Mathematics 9, no. 3 (2000): 435–55. http://dx.doi.org/10.1080/10586458.2000.10504420.

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39

Zinger, Aleksey. "Enumerative vs.\ symplectic invariants and obstruction bundles." Journal of Symplectic Geometry 2, no. 4 (2004): 445–543. http://dx.doi.org/10.4310/jsg.2004.v2.n4.a1.

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40

Gorbunov, Vassily, and Nigel Ray. "Orientations of Spin bundles and symplectic cobordism." Publications of the Research Institute for Mathematical Sciences 28, no. 1 (1992): 39–55. http://dx.doi.org/10.2977/prims/1195168855.

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41

Hurtubise, J. C., and L. C. Jeffrey. "Representations with Weighted Frames and Framed Parabolic Bundles." Canadian Journal of Mathematics 52, no. 6 (2000): 1235–68. http://dx.doi.org/10.4153/cjm-2000-052-4.

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AbstractThere is a well-known correspondence (due to Mehta and Seshadri in the unitary case, and extended by Bhosle and Ramanathan to other groups), between the symplectic variety Mh of representations of the fundamental group of a punctured Riemann surface into a compact connected Lie group G, with fixed conjugacy classes h at the punctures, and a complex variety of holomorphic bundles on the unpunctured surface with a parabolic structure at the puncture points. For G = SU(2), we build a symplectic variety P of pairs (representations of the fundamental group into G, “weighted frame” at the pu

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42

MARTÍNEZ TORRES, DAVID. "NONLINEAR SYMPLECTIC GRASSMANNIANS AND HAMILTONIAN ACTIONS IN PREQUANTUM LINE BUNDLES." International Journal of Geometric Methods in Modern Physics 09, no. 01 (2012): 1250001. http://dx.doi.org/10.1142/s0219887812500016.

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In this paper we extend to the Fréchet setting the following well-known fact about finite-dimensional symplectic geometry: if a Lie group G acts on a symplectic manifold in a Hamiltonian fashion with momentum map μ, given x ∈ M the isotropy group Gx acts linearly on the tangent space in a Hamiltonian fashion, with momentum map the Taylor expansion of μ up to degree 2. We use this result to give a conceptual explanation for a formula of Donaldson in [Scalar curvature and projective embeddings. I, J. Differential Geom.59(3) (2001) 479–522], which describes the momentum map of the Hamiltonian inf

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43

Moraru, Ruxandra. "Integrable Systems Associated to a Hopf Surface." Canadian Journal of Mathematics 55, no. 3 (2003): 609–35. http://dx.doi.org/10.4153/cjm-2003-025-3.

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AbstractA Hopf surface is the quotient of the complex surface by an infinite cyclic group of dilations of . In this paper, we study the moduli spaces of stable -bundles on a Hopf surface , from the point of view of symplectic geometry. An important point is that the surface is an elliptic fibration, which implies that a vector bundle on can be considered as a family of vector bundles over an elliptic curve. We define a map that associates to every bundle on a divisor, called the graph of the bundle, which encodes the isomorphism class of the bundle over each elliptic curve. We then prove that

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44

Baracco, Luca, and Giuseppe Zampieri. "Analytic discs in symplectic spaces." Nagoya Mathematical Journal 161 (March 2001): 55–67. http://dx.doi.org/10.1017/s0027763000022121.

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We develop some symplectic techniques to control the behavior under symplectic transformation of analytic discs A of X = ℂn tangent to a real generic submanifold R and contained in a wedge with edge R.We show that if A* is a lift of A to T* X and if χ is a symplectic transformation between neighborhoods of po and qo, then A is orthogonal to po if and only if Ã:= πχA* is orthogonal to qo. Also we give the (real) canonical form of the couples of hypersurfaces of ℝ2n ⋍ ℂn whose conormal bundles have clean intersection. This generalizes [10] to general dimension of intersection.Combining this resu

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45

Grady, Ryan, and Owen Gwilliam. "LIE ALGEBROIDS AS SPACES." Journal of the Institute of Mathematics of Jussieu 19, no. 2 (2018): 487–535. http://dx.doi.org/10.1017/s1474748018000075.

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In this paper, we relate Lie algebroids to Costello’s version of derived geometry. For instance, we show that each Lie algebroid – and the natural generalization to dg Lie algebroids – provides an (essentially unique) $L_{\infty }$ space. More precisely, we construct a faithful functor from the category of Lie algebroids to the category of $L_{\infty }$ spaces. Then we show that for each Lie algebroid $L$, there is a fully faithful functor from the category of representations up to homotopy of $L$ to the category of vector bundles over the associated $L_{\infty }$ space. Indeed, this functor s

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46

Kucharz, Wojciech. "Symplectic complex bundles over real algebraic four-folds." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 47, no. 3 (1989): 430–37. http://dx.doi.org/10.1017/s1446788700033152.

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AbstractLetXbe a compact affine real algebraic variety of dimension 4. We compute the Witt group of symplectic bilinear forms over the ring of regular functions fromXto C. The Witt group is expressed in terms of some subgroups of the cohomology groups.

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47

Kim, Hoil. "Moduli spaces of stable vector bundles on Enriques surfaces." Nagoya Mathematical Journal 150 (June 1998): 85–94. http://dx.doi.org/10.1017/s002776300002506x.

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Abstract.We show that the image of the moduli space of stable bundles on an Enriques surface by the pull back map is a Lagrangian subvariety in the moduli space of stable bundles, which is a symplectic variety, on the covering K3 surface. We also describe singularities and some other features of it.

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48

BHOSLE, USHA, INDRANIL BISWAS, and JACQUES HURTUBISE. "GRASSMANNIAN-FRAMED BUNDLES AND GENERALIZED PARABOLIC STRUCTURES." International Journal of Mathematics 24, no. 12 (2013): 1350090. http://dx.doi.org/10.1142/s0129167x13500900.

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We build compact moduli spaces of Grassmannian-framed bundles over a Riemann surface, essentially replacing a group by a bi-equivariant compactification. We do this both in the algebraic and symplectic settings, and prove a Hitchin–Kobayashi correspondence between the two. The spaces are universal spaces for parabolic bundles (in the sense that all of the moduli can be obtained as quotients), and the reduction to parabolic bundles commutes with the correspondence. An analogous correspondence is outlined for the generalized parabolic bundles of Bhosle.

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49

Esen, Oğul, Hasan Gümral, and Serkan Sütlü. "Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles." Theoretical and Applied Mechanics 48, no. 2 (2021): 201–36. http://dx.doi.org/10.2298/tam210312009e.

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Given a Lie group ??, we elaborate the dynamics on ??*??*?? and ??*????, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space ????*??, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics.

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Christian, Austin. "On symplectic fillings of virtually overtwisted torus bundles." Algebraic & Geometric Topology 21, no. 1 (2021): 469–505. http://dx.doi.org/10.2140/agt.2021.21.469.

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