Дисертації з теми "G-bundles"

Denotemos por X ~ p \'S POT. m\' x \'S POT. n\' um espaço finitístico com anel de cohomologia módulo p isomorfo ao anel de cohomologia de um produto de esferas \'S POT. m\' x \'S POT. n\', o qual admite ação livre do grupo cíclico G = Zp, com p um primo ímpar. Nosso objetivo neste trabalho é determinar o anel de cohomologia do espaço de órbitas X / G, usando como ferramenta principal a seqüência espectral de Leray-Serre associada à fibração de Borel X \'SETA\' \'imath\' X G \'SETA\' \'pi\' B G, onde BG é o espaço classificante do G-fibrado universal wG = (EG;BG; pG; G;G) e XG = EG x G X é o espaço de Borel. Este resultado foi provado por R. M. Dotzel, T. B. Singh and S. P. Tripathi em [14]
Let denote by X ~ p \'S POT. m\' x \'S POT. n\' finitistic space with mod p cohomology ring isomorphic to the cohomology ring of a product of spheres \'S POT. m\' x \'S POT. n\' , which admits a free action of the cyclic group G = Zp, with p an odd prime. Our goal in this work is to determine the cohomology ring of the orbit space X / G, using as main tool the Leray-Serre spectral sequence associated to the Borel fibration X \'SETA\" \'imath\' \'X G \'SETA\' \'pi\' BG, where BG is the classifying space of the G-universal bundle wG = (EG;BG; pG; G;G) and XG = EG x G X is the Borel space. This result was proved by R. M. Dotzel, T. B. Singh and S. P. Tripathi in [14]

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.

It is well-known that del Pezzo surfaces of degree 9 -- n. are in one-to-one correspondence to flat En bundles over elliptic curves which are anti-canonical curves of such surfaces. In my thesis, we study a broader class of rational surfaces which are called ADE surfaces. We construct Lie algebra bundles of any type on these surfaces, and extend the above correspondence to flat G bundles over elliptic curves, where G is a simple, compact and simply-connected Lie group of any type. Concretely, we establish a natural identification between the following two very different moduli spaces for a Lie group G of any type: the moduli space of rational surfaces with G-configurations and the moduli space of flat G-bundles over a fixed elliptic curve.
Zhang, Jiajin.
"July 2007."
Adviser: Leung Nai Chung Conan.
Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0357.
Thesis (Ph.D.)--Chinese University of Hong Kong, 2007.
Includes bibliographical references (p. 77-79).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts in English and Chinese.
School code: 1307.

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.