Thesis advisor: Avner D. Ash / We analyze the overconvergent cohomology modules introduced by Ash and Stevens, applying them to construct eigenvarieties for fairly general reductive groups. We then establish several instances of p-adic Langlands functoriality for these eigenvarieties, and we use these functorialities to give evidence for a precise conjecture relating trianguline Galois representations to overconvergent cohomology classes. Our main technical innovations are a family of universal coefficients spectral sequences for overconvergent cohomology and a generalization of Chenevier's interpolation theorem. / Thesis (PhD) — Boston College, 2013. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

In this work we study the space of group homomorphisms Hom(Γ,G) from a geometric and simplicial point of view. The case in which the source group is a free abelian group of rank n is studied in more detail since this space can be identified with the space of commuting n-tuples of elements from G. This latter case is of particular interest when the target is a Lie group. The simplicial approach allows us to to construct a family of spaces that filters the classifying space of a group by filtering group theoretical information of the given group. Namely, we use the lower central series of free groups to construct a family of simplicial subspaces of the bar construction of the classifying space of a group. The first layer of this filtration is studied in more detail for transitively commutative (TC) groups.

In this work we study the space of group homomorphisms Hom(Γ,G) from a geometric and simplicial point of view. The case in which the source group is a free abelian group of rank n is studied in more detail since this space can be identified with the space of commuting n-tuples of elements from G. This latter case is of particular interest when the target is a Lie group. The simplicial approach allows us to to construct a family of spaces that filters the classifying space of a group by filtering group theoretical information of the given group. Namely, we use the lower central series of free groups to construct a family of simplicial subspaces of the bar construction of the classifying space of a group. The first layer of this filtration is studied in more detail for transitively commutative (TC) groups.

Equivariant localisation is based on exploiting certain symmetries of some systems, generally represented by a non-free action of a Lie group on a manifold, to reduce the dimensionality of integral calculations that commonly appear in theoretical physics. In this work we present Cartan's model of equivariant cohomology in different scenarios, such as differential manifolds, symplectic manifolds or vector bundles and we reproduce the main corresponding localisation results.

No description available.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2004. / Includes bibliographical references (p. 87-89).

Thesis (Ph. D.)--University of Oregon, 2000. / Includes vita and abstract. Includes bibliographical references (leaf 91). Also available for download via the World Wide Web; free to University of Oregon users.

Thesis (Ph. D.)--University of Oregon, 2000. / Title from title screen. Paging within document: vii, 91 p. Includes vita and abstract. Includes bibliographical references (p. 91).

In this work we study the space of group homomorphisms Hom(Γ,G) from a geometric and simplicial point of view. The case in which the source group is a free abelian group of rank n is studied in more detail since this space can be identified with the space of commuting n-tuples of elements from G. This latter case is of particular interest when the target is a Lie group. The simplicial approach allows us to to construct a family of spaces that filters the classifying space of a group by filtering group theoretical information of the given group. Namely, we use the lower central series of free groups to construct a family of simplicial subspaces of the bar construction of the classifying space of a group. The first layer of this filtration is studied in more detail for transitively commutative (TC) groups. / Science, Faculty of / Mathematics, Department of / Graduate

Neste trabalho, estudamos a cohomologia de de Rham e métodos para os seus cálculos. Finalizamos com aplicações da cohomologia de de Rham em teoremas da topologia / In this work we study the de Rham cohomology and methods for its calculations. We close it with applications of the Rham cohomology in theorems from topology