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Spaces of homomorphisms and group cohomology

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.

  1. http://hdl.handle.net/2429/224
Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:BVAU./224
Date05 1900
CreatorsTorres Giese, Enrique
PublisherUniversity of British Columbia
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Format431727 bytes, application/pdf

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