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Spaces of homomorphisms and group cohomology

University of British Columbia

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.

Thesis/Dissertation

application/pdf

2007-12-18

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/224

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/