Дисертації з теми "Symplectic bundles"
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1
at, Andreas Cap@esi ac. "Equivariant Symplectic Geometry of Cotangent Bundles." Moscow Math. J. 1, No.2 (2001) 287-299, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi996.ps.
Повний текст джерела
2
Hitching, George H. "Moduli of symplectic bundles over curves." Thesis, Durham University, 2005. http://etheses.dur.ac.uk/2351/.
Повний текст джерелаАнотація:
Let Х be a complex projective smooth irreducible curve of genus g. We begin by giving background material on symplectic vector bundles and principal bundles over X and introduce the moduli spaces we will be studying, In Chapter 2 we describe the stable singular locus and semistable boundary of the moduli space Mx(Sp2 C) of semistable principal Sp2 C-bundles over X. In Chapter 3 we give results on symplectic extensions and Lagrangian subbundles. In Chapter 4, we assemble some results on vector bundles of rank 2 and degree 1 over a curve of genus 2, which are needed in what follows. Chapter 5 describes a generically finite cover of Aix(Sp2C) for a curve of genus 2. In the last chapter, we give some results on theta-divisors of rank 4 symplectic vector bundles over curves: we prove that the general such bundle over a curve of genus 2 possesses a theta-divisor, and characterise those stable bundles with singular theta-divisors. Many results on symplectic bundles admit analogues in the orthogonal case, which we have outlined where possible.
3
Henriksen, Tobias Våge. "Symplectic Homology and Shape of Cotangent Bundles." Thesis, Uppsala universitet, Algebra och geometri, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-451813.
Повний текст джерела
4
Plummer, Michael. "Stratified fibre bundles and symplectic reduction on coadjoint orbits of SU(n)." Thesis, University of Surrey, 2008. http://epubs.surrey.ac.uk/842671/.
Повний текст джерелаАнотація:
The problem of classifying the reduced phase spaces of the natural torus action on a generic coadjoint orbit of SU(n) is considered. The concept of a stratified fibre bundle is defined. It is proved that the orbit map of an equivariant fibre bundle is a stratified fibre bundle. This result is then used to give an iterative description of the reduced phase spaces of the torus action on a generic coadjoint orbit of SU(n). The theory is illustrated with a detailed examination of the n = 3 case, that of the two torus action on a coadjoint orbit of SU(3).
5
Kirchhoff-Lukat, Charlotte Sophie. "Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283007.
Повний текст джерелаАнотація:
This thesis explores aspects of generalized geometry, a geometric framework introduced by Hitchin and Gualtieri in the early 2000s. In the first part, we introduce a new class of submanifolds in stable generalized complex manifolds, so-called Lagrangian branes with boundary. We establish a correspondence between stable generalized complex geometry and log symplectic geometry, which allows us to prove results on local neighbourhoods and small deformations of this new type of submanifold. We further investigate Lefschetz thimbles in stable generalized complex Lefschetz fibrations and show that Lagrangian branes with boundary arise in this context. Stable generalized complex geometry provides the simplest examples of generalized complex manifolds which are neither complex nor symplectic, but it is sufficiently similar to symplectic geometry for a multitude of symplectic results to generalize. Our results on Lefschetz thimbles in stable generalized complex geometry indicate that Lagrangian branes with boundary are part of a potential generalisation of the Wrapped Fukaya category to stable generalized complex manifolds. The work presented in this thesis should be seen as a first step towards the extension of Floer theory techniques to stable generalized complex geometry, which we hope to develop in future work. The second part of this thesis studies Dorfman brackets, a generalisation of the Courant- Dorfman bracket, within the framework of double vector bundles. We prove that every Dorfman bracket can be viewed as a restriction of the Courant-Dorfman bracket on the standard VB-Courant algebroid, which is in this sense universal. Dorfman brackets have previously not been considered in this context, but the results presented here are reminiscent of similar results on Lie and Dull algebroids: All three structures seem to fit into a more general duality between subspaces of sections of the standard VB-Courant algebroid and brackets on vector bundles of the form T M ⊕ E ∗ , E → M a vector bundle. We establish a correspondence between certain properties of the brackets on one, and the subspaces on the other side.
6
Choy, Jaeyoo. "Moduli spaces of framed symplectic and orthogonal bundles on P2 and the K-theoretic Nekrasov partition functions." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/198873.
Повний текст джерела
7
Karlsson, Cecilia. "Orienting Moduli Spaces of Flow Trees for Symplectic Field Theory." Doctoral thesis, Uppsala universitet, Algebra och geometri, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-269551.
Повний текст джерелаАнотація:
This thesis consists of three scientific papers dealing with invariants of Legendrian and Lagrangian submanifolds. Besides the scientific papers, the thesis contains an introduction to contact and symplectic geometry, and a brief outline of Symplectic field theory with focus on Legendrian contact homology. In Paper I we give an orientation scheme for moduli spaces of rigid flow trees in Legendrian contact homology. The flow trees can be seen as the adiabatic limit of sequences of punctured pseudo-holomorphic disks with boundary on the Lagrangian projection of the Legendrian. So to equip the trees with orientations corresponds to orienting the determinant line bundle of the dbar-operator over the space of Lagrangian boundary conditions on the punctured disk. We define an orientation of this line bundle and prove that it is well-defined in the limit. We also prove that the chosen orientation scheme gives rise to a combinatorial algorithm for computing the orientation of the trees, and we give an explicit description of this algorithm. In Paper II we study exact Lagrangian cobordisms with cylindrical Legendrian ends, induced by Legendrian isotopies. We prove that the combinatorially defined DGA-morphisms used to prove invariance of Legendrian contact homology for Legendrian knots over the integers can be derived analytically. This is proved using the orientation scheme from Paper I together with a count of abstractly perturbed flow trees of the Lagrangian cobordisms. In Paper III we prove a flexibility result for closed, immersed Lagrangian submanifolds in the standard symplectic plane.
8
Monzner, Alexandra [Verfasser], Karl Friedrich [Akademischer Betreuer] Siburg, and Lorenz Johannes [Akademischer Betreuer] Schwachhöfer. "Partial quasi-morphisms and symplectic quasi-integrals on cotangent bundles / Alexandra Monzner. Betreuer: Karl Friedrich Siburg. Gutachter: Lorenz Johannes Schwachhöfer." Dortmund : Universitätsbibliothek Dortmund, 2012. http://d-nb.info/1099912598/34.
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9
MOSSA, ROBERTO. "Balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space." Doctoral thesis, Università degli Studi di Cagliari, 2011. http://hdl.handle.net/11584/266274.
Повний текст джерелаАнотація:
This thesis deals with two different subjects: balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space. Correspondingly we have two main results. In the first one we prove that if a holomorphic vector bundle E over a compact Kähler manifold (M,ω) admits a ω-balanced metric then this metric is unique. In the second one, after defining the diastatic exponential of a real analytic Kähler manifold, we
prove that for every point p of an Hermitian symmetric space of noncompact type there exists a globally defined diastatic exponential centered in p which is a diffeomorphism and it is uniquely determined by its restriction to polydisks.
10
Kennedy, Chris A. "Construction of Maps by Postnikov Towers." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1533034197206461.
Повний текст джерела
11
Branco, Lucas Magalhães Pereira Castello 1988. "Mapas momento em teoria de calibre." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306010.
Повний текст джерелаАнотація:
Orientador: Marcos Benevenuto JardimDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
Made available in DSpace on 2018-08-22T22:29:57Z (GMT). No. of bitstreams: 1 Branco_LucasMagalhaesPereiraCastello_M.pdf: 1981391 bytes, checksum: 7ecd7674514f634b8bb527c0bcab1a06 (MD5) Previous issue date: 2013
Resumo: Neste trabalho os aspectos básicos da teoria de calibre são abordados, incluindo as noções de conexão e curvatura em fibrados principais e vetoriais, considerações sobre o grupo de transformações de calibre e o espaço de moduli de soluções para a equação anti-auto-dual em dimensão quatro (o espaço de moduli de instantons). Posteriormente, mapas momento e redução são introduzidos. Primeiramente, no contexto clássico de geometria simplética e depois no contexto de geometria hyperkähler. Por fim, são apresentadas aplicações da teoria de mapas momento e redução em teoria de calibre. As equações ADHM são introduzidas e mostra se que estas podem ser dadas como o conjunto de zeros de um mapa momento hyperkähler. Além disso, considerações são feitas acerca da construção ADHM de instantons, que relaciona soluções dessas equações com as soluções da equação de anti-auto-dualidade. O espaço de moduli de conexões planas é também abordado. Neste caso, a curvatura é vista como um mapa momento e os cálculos podem ser generalizados para o espaço de moduli de conexões planas sobre variedades Kähler de dimensões mais altas e para o espaço de moduli de instantons sobre variedades hyperkähler de dimensão quatro
Abstract: In this work it is developed the basic concepts of gauge theory, including the notions of connections and curvature on principal bundles and vector bundles, considerations on the group of gauge transformations and the moduli space of anti-self-dual connections in dimension four (the instanton moduli space). After, moment maps and reduction are introduced. First in the classical context of symplectic geometry, then in hyperkähler geometry. At last, applications to the theory of moment maps and reduction in gauge theory are given. The ADHM equations are introduced and it is shown that solutions to these equations can be given by the zeros of a hyperkähler moment map. Furthermore, the ADHM construction, that relates the ADHM equations to instanton solutions, is discussed. The moduli space of flat connections over a Riemann surface is also treated. In this case, the curvature is seen as a moment map and the calculations can be generalized to flat connections over higher-dimensional Kähler manifolds and to the instanton moduli space over four dimensional hyperkähler manifolds
Mestrado
Matematica
Mestre em Matemática
12
Hedlund, William. "Geometric Quantization." Thesis, Uppsala universitet, Teoretisk fysik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-325649.
Повний текст джерелаАнотація:
We formulate a process of quantization of classical mechanics, from a symplecticperspective. The Dirac quantization axioms are stated, and a satisfactory prequantizationmap is constructed using a complex line bundle. Using polarization, it isdetermined which prequantum states and observables can be fully quantized. Themathematical concepts of symplectic geometry, fibre bundles, and distributions are exposedto the degree to which they occur in the quantization process. Quantizationsof a cotangent bundle and a sphere are described, using real and K¨ahler polarizations,respectively.
13
Fedosov, Boris. "Moduli spaces and deformation quantization in infinite dimensions." Universität Potsdam, 1998. http://opus.kobv.de/ubp/volltexte/2008/2539/.
Повний текст джерелаАнотація:
We construct a deformation quantization on an infinite-dimensional symplectic space of regular connections on an SU(2)-bundle over a Riemannian surface of genus g ≥ 2. The construction is based on the normal form thoerem representing the space of connections as a fibration over a finite-dimensional moduli space of flat connections whose fibre is a cotangent bundle of the infinite-dimensional gauge group. We study the reduction with respect to the gauge groupe both for classical and quantum cases and show that our quantization commutes with reduction.
14
Bauer, David. "Towards Discretization by Piecewise Pseudoholomorphic Curves." Doctoral thesis, Universitätsbibliothek Leipzig, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-132065.
Повний текст джерелаАнотація:
This thesis comprises the study of two moduli spaces of piecewise J-holomorphic curves. The main scheme is to consider a subdivision of the 2-sphere into a collection of small domains and to study collections of J-holomorphic maps into a symplectic manifold. These maps are coupled by Lagrangian boundary conditions. The work can be seen as finding a 2-dimensional analogue of the finite-dimensional path space approximation by piecewise geodesics on a Riemannian manifold (Q,g).
For a nice class of target manifolds we consider tangent bundles of Riemannian manifolds and symplectizations of unit tangent bundles. Via polarization they provide a rich set of Lagrangians which can be used to define appropriate boundary value problems for the J-holomorphic pieces. The work focuses on existence theory as a pre-stage to global questions such as combinatorial refinement and the quality of the approximation.
The first moduli space of lifted type is defined on a triangulation of the 2-sphere and consists of disks in the tangent bundle whose boundary projects onto geodesic triangles. The second moduli space of punctured type is defined on a circle packing domain and consists of boundary punctured disks in the symplectization of the unit tangent bundle. Their boundary components map into single fibers and at punctures the disks converge to geodesics. The coupling boundary conditions are chosen such that the piecewise problem always is Fredholm of index zero and both moduli spaces only depend on discrete data.
For both spaces existence results are established for the J-holomorphic pieces which hold true on a small scale. Each proof employs a version of the implicit function theorem in a different setting. Here the argument for the moduli space of punctured type is more subtle. It rests on a connection to tropical geometry discovered by T. Ekholm for 1-jet spaces. The boundary punctured disks are constructed in the vicinity of explicit Morse flow trees which correspond to the limiting objects under degeneration of the boundary condition.
15
Bouali, Johann. "Motifs des fibrés en quadriques et jacobiennes intermédiaires relatives des paires K3-Fano." Thesis, Dijon, 2015. http://www.theses.fr/2015DIJOS021/document.
Повний текст джерелаАнотація:
Cette thèse comporte deux parties. Dans la première partie on étudie le motif de Chow d’un fibré en quadriques de dimension relative impaire sur une surface. On montre que ce motif admet une décomposition qui fait intervenir le motif de Prym du revêtement double de la courbe discriminante. Dans la deuxième partie on s’intéresse à des fibrations lagrangiennes, obtenues comme jacobiennes intermédiaires relatives des familles de variétés de Fano de dimension trois contenant une surface K3 fixée, et à l’existence d’une compactification symplectique. Dans un cas particulier, on étudie une compactification partielle en utilisant des calculs avec le logiciel Macaulay2This thesis consists of two parts. In the first part we study the Chow motive of a quadric bundle of odd relative dimension over a surface. We show that this motive admits a decomposition which involves the Prym motive of the double covering of the discriminant curve.In the second part, we consider Lagrangian fibrations, obtained as relative intermediate Jacobians of families of Fano threefolds containing a fixed K3 surface, and the existence of a symplectic compactification. In a particular case, we study a partial compactification using calculations with the software system Macaulay2
16
Toko, Wilson Bombe. "Bundles in the category of Frölicher spaces and symplectic structure." Thesis, 2008. http://hdl.handle.net/10539/5860.
Повний текст джерелаАнотація:
Bundles and morphisms between bundles are defined in the category of
Fr¨olicher spaces (earlier known as the category of smooth spaces, see [2], [5],
[9], [6] and [7]). We show that the sections of Fr¨olicher bundles are Fr¨olicher
smooth maps and the fibers of Fr¨olicher bundles have a Fr¨olicher structure.
We prove in detail that the tangent and cotangent bundles of a n-dimensional
pseudomanifold are locally diffeomorphic to the even-dimensional Euclidian
canonical F-space R2n. We define a bilinear form on a finite-dimensional
pseudomanifold. We show that the symplectic structure on a cotangent bundle
in the category of Fr¨olicher spaces exists and is (locally) obtained by the
pullback of the canonical symplectic structure of R2n. We define the notion
of symplectomorphism between two symplectic pseudomanifolds. We prove
that two cotangent bundles of two diffeomorphic finite-dimensional pseudomanifolds
are symplectomorphic in the category of Frölicher spaces.
17
Krepski, Derek. "Pre-quantization of the Moduli Space of Flat G-bundles." Thesis, 2009. http://hdl.handle.net/1807/19047.
Повний текст джерелаАнотація:
This thesis studies the pre-quantization of quasi-Hamiltonian group actions from a
cohomological viewpoint. The compatibility of pre-quantization with symplectic reduction
and the fusion product are established, and are used to understand the necessary and sufficient conditions for the pre-quantization of M(G,S), the moduli space of
at flat G-bundles over a closed surface S.
For a simply connected, compact, simple Lie group G, M(G,S) is known to be pre-quantizable at integer levels. For non-simply connected G, however, integrality of the level is not sufficient for pre-quantization, and this thesis determines the obstruction, namely a certain 3-dimensional cohomology class, that places further restrictions on the underlying level. The levels that admit a pre-quantization of the moduli space are
determined explicitly for all non-simply connected, compact, simple Lie groups G. Partial results are obtained for the case of a surface S with marked points.
Also, it is shown that via the bijective correspondence between quasi-Hamiltonian
group actions and Hamiltonian loop group actions, the corresponding notions of prequantization coincide.
18
Connery-Grigg, Dustin. "Fibrés symplectiques et la géométrie des difféomorphismes hamiltoniens." Thèse, 2016. http://hdl.handle.net/1866/18774.
Повний текст джерелаАнотація:
Ce mémoire porte sur quelques éléments de la théorie des fibrés symplectiques et leurs usages en étudiant la géométrie hoferienne sur le groupe de difféomorphismes hamiltoniens. En particulier en assumant un certain confort avec les notions de base de la géométrie différentielle et de la topologie algébrique on développe dans le premier chapitre les rudiments nécessaires de la théorie des G-fibrés et, dans la deuxième, tous les faits nécessaires de la topologie symplectique et les difféomorphismes hamiltoniens pour comprendre la théorie de base des fibrés symplectiques, à voir le morphisme de flux et ses liens aux isotopies hamiltoniennes. Le troisième chapitre présente les fondements des fibrés symplectiques se conclu en construisant la forme de couplage dans un langage invariant et en présentant la caractérisation des fibrés symplectiques, dont le groupe de structure réduit au groupe hamiltonien. Le mémoire se termine en présentant quelques applications des fibrés hamiltoniens à la géométrie de Hofer, en particulier une caractérisation de la partie positive de la norme de Hofer d'un lacet hamiltonien en termes du K-aire du fibré au-dessus de la sphère associé et une démonstration de la non-dégénérescence de la norme de Hofer pour des variétés symplectiques fermées.This thesis presents a reasonably complete account of the elements theory of symplectic and Hamiltonian fibrations. We assume a familiarity and comfort with the basic notions of differential geometry and algebraic topology but little else. Proceeding from this, the first chapter develops the necessary notions from the theory of fiber bundles and G-fiber bundles, while the second chapter develops all the notions and theorems required to understand the later theory of symplectic fibrations. Most notably the second chapter includes a detailed account of the classical relationship between the flux homomorphism and Hamiltonian isotopies. The third chapter is where we develop the theory of symplectic and locally Hamiltonian fiber bundles, and in particular give an invariant construction of the coupling form on a symplectic fibration admitting an extension class. the third chapter ends with a proof of a structure theorem characterizing those symplectic fibrations for which the structure group reduces to the Hamiltonian group. In the final chapter, we present some applications of the theory of Hamiltonian fibrations by the way of characterizing the positive part of the Hofer norm of a Hamiltonian loop as the K-area of its associated Hamiltonian bundle over the sphere, and we finish by giving a proof of the non-degeneracy of the Hofer norm for closed symplectic manifolds.
19
Chassé, Jean-Philippe. "Sur le h-principe pour les immersions coisotropes et les classes caractéristiques associées." Thèse, 2018. http://hdl.handle.net/1866/22134.
Повний текст джерела
20
Bauer, David. "Towards Discretization by Piecewise Pseudoholomorphic Curves." Doctoral thesis, 2012. https://ul.qucosa.de/id/qucosa%3A12277.
Повний текст джерелаАнотація:
This thesis comprises the study of two moduli spaces of piecewise J-holomorphic curves. The main scheme is to consider a subdivision of the 2-sphere into a collection of small domains and to study collections of J-holomorphic maps into a symplectic manifold. These maps are coupled by Lagrangian boundary conditions. The work can be seen as finding a 2-dimensional analogue of the finite-dimensional path space approximation by piecewise geodesics on a Riemannian manifold (Q,g).
For a nice class of target manifolds we consider tangent bundles of Riemannian manifolds and symplectizations of unit tangent bundles. Via polarization they provide a rich set of Lagrangians which can be used to define appropriate boundary value problems for the J-holomorphic pieces. The work focuses on existence theory as a pre-stage to global questions such as combinatorial refinement and the quality of the approximation.
The first moduli space of lifted type is defined on a triangulation of the 2-sphere and consists of disks in the tangent bundle whose boundary projects onto geodesic triangles. The second moduli space of punctured type is defined on a circle packing domain and consists of boundary punctured disks in the symplectization of the unit tangent bundle. Their boundary components map into single fibers and at punctures the disks converge to geodesics. The coupling boundary conditions are chosen such that the piecewise problem always is Fredholm of index zero and both moduli spaces only depend on discrete data.
For both spaces existence results are established for the J-holomorphic pieces which hold true on a small scale. Each proof employs a version of the implicit function theorem in a different setting. Here the argument for the moduli space of punctured type is more subtle. It rests on a connection to tropical geometry discovered by T. Ekholm for 1-jet spaces. The boundary punctured disks are constructed in the vicinity of explicit Morse flow trees which correspond to the limiting objects under degeneration of the boundary condition.