UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Spaces of homomorphisms and group cohomology Torres Giese, Enrique

Abstract

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.

Item Citations and Data

License

Attribution-NonCommercial-NoDerivatives 4.0 International

Usage Statistics