Thesis (Ph. D.)--University of Wisconsin--Madison, 1962. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaf [56]).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1965. / Typescript. Vita. Description based on print version record. Includes bibliographies: leaves 56-57, 72.

This thesis deals with generalized fibre spaces. It improves upon existing definitions and introduces new ones. It establishes the category of pairs and the category of g.f.s. The relationship between classical fibre spaces and generalized fibre spaces is examined. The induced g.f.s. is defined as well as the concept of section and it is established that the lifting of a fully regular continuous g-function is equivalent to the existence of a section in the induced g.f.s. Finally the lifting theorem for g.f.s. is stated and proved. / Thesis / Doctor of Philosophy (PhD)

Orientador: Marcos Benevuto Jardim / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-08T04:40:41Z (GMT). No. of bitstreams: 1 Frejlich_Pedro_M.pdf: 852390 bytes, checksum: bcde0cd89c0bcfe3b2515b5cfe48e528 (MD5) Previous issue date: 2007 / Resumo: Construímos a transformada de Nahm de um fibrado de Higgs estável de grau nulo sobre uma superfície de Riemann de gênero pelo menos 2. Para tanto, empregamos a Teoria do Índice de Atiyah-Singer e um vanishing theorem que segue da hipótese de estabilidade do fibrado. O principal resultado é que o fibrado transformado é hiperholomorfo e sem fatores planos. Desse modo não só recuperamos os resultados algébricos de [7] e os de [12] para o cos q = 0 como também provamos uma descrição mais detalhada da estrutura geométrica da transformada ¿ o que, aliada às técnicas de [10] sugere que ela possa ser invertida. Palavras-chave: Superfícies de Riemann, Fibrados Estáveis, Teoria do Índice, Transformada de Nahm, Transformada de Fourier-Mukai, Variedades Hiper-Kähler, Variedades Abelianas, Conexões Hiperholomorfas / Abstract: We construct the Nahm transform of a stable, degree-zero Higgs bundle on a Riemann surface of genus at least 2. Atiyah-Singer¿s index theorem is the basic tool employed, along with a vanishing theorem which is due to the stability hypothesis. Our main result is that the transformed bundle is hyperholomorphic and without flat factors. This not only recovers the algebraic results of [7] and that of [12] for the cos q = 0, but also provides a more detailed description of the geometric structure of the transformed bundle. Such results suggest that this Nahm transform can be inverted, cf. [10]. Key-words:Riemann surfaces, Stable bundles, Index Theory, Nahm Transform, Fourier-Mukai Transform, Hyperk¨ahler manifolds, Abelian varieties, Hyperholomorphic connections / Mestrado / Geometria Diferencial/Geometria algebrica / Mestre em Matemática