{"id":{"repo_id":"ubc","oai_identifier":"oai:circle.library.ubc.ca:2429/224"},"canonical_url":"https://search.dev.ndltd.org/etd/ubc/oai:circle.library.ubc.ca:2429/224","repository":{"repo_id":"ubc","name":"University of British Columbia","base_url":"http://circle.library.ubc.ca/oai/request"},"display":{"title":"Spaces of homomorphisms and group cohomology","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. 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