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
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/224 |
| Date | 05 1900 |
| Creators | Torres Giese, Enrique |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Format | 431727 bytes, application/pdf |
| Rights | Attribution-NonCommercial-NoDerivatives 4.0 International, http://creativecommons.org/licenses/by-nc-nd/4.0/ |
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