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.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:BVAU.2429/224 |
| Date | 05 1900 |
| Creators | Torres Giese, Enrique |
| Publisher | University of British Columbia |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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