Un arrangement central A est un ensemble fini de sous-espaces vectoriels dans un espace vectoriel complexe V de dimension finie. L'espace topologique complémentaire M(A) est l'ensemble des points de V qui n'appartiennent à aucun des sous-espaces de A. Dans ce travail, nous étudions la topologie de l'espace M(A) du point de vue de l'homotopie rationnelle. L'outil clé qui a servi de départ à cette thèse est un modèle rationnel de M(A) qui s'avère relativement simple à manipuler. À l'aide de ce modèle, nous obtenons plusieurs résultats sur la topologie de M(A). Citons par exemple des formules de récursion qui permettent de calculer certains invariants topologiques, dont les nombres de Betti, une preuve du fait que la caractéristique d'Euler de l'espace M(A) est nulle ou encore une description des arrangements (vérifiant une condition technique) dont le complémentaire est un wedge rationnel de sphères. Enfin, les résultats principaux de cet ouvrage sont une caractérisation des arrangements dont le complémentaire a le type d'homotopie d'un produit de sphères, et la preuve du fait que si le complémentaire n'est pas un produit de sphères, alors son algèbre de Lie d'homotopie contient la sous-algèbre de Lie libre à deux générateurs.

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The main purpose of this work is to study model category structures (in the sense of Quillen) on the categories of small categories and small symmetric multicategories enriched over an arbitrary monoidal model category. Among these model structures, there is one of the greatest importance in applications. We call it the Dwyer-Kan model structure (for enriched categories or enriched symmetric multicategories), and a large amount of this work is dedicated to establishing it for different choices of monoidal model categories. Another model structure that we study is what we call the fibred model structure, again for both small categories and small symmetric multicategories enriched over a suitable monoidal model category. / The other purpose of this work is to study model category structures on the category of comonoids in a monoidal model category.

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.

Thesis (Ph. D.)--Oregon State University, 1990. / Typescript (photocopy). Includes bibliography (leaves 65-67). Also available on the World Wide Web.

Thesis (Ph. D.)--Michigan State University. Dept. of Mathematics, 2008. / Title from PDF t.p. (viewed Aug. 17, 2009). Includes bibliographical references (p. 84-87). Also issued in print.

Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, June 2003. / Includes bibliographical references. Also available on the Internet.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1997. / Includes bibliographical references (p. 72-74).

Thesis (Ph. D.)--University of Wisconsin--Madison, 1967. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

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