2:00 pm Monday, February 23, 2015
Topology Seminar: The Topology of Representation Varieties by Maxime Bergeron (University of British Columbia) in RLM 12.166
Let N be a finitely generated group and let G be a complex reductive linear algebraic group (e.g. a special linear group). The representation space Hom(N,G), carved out of a finite product of copies of G by the relations of N, has many interesting topological features. From the point of view of algebraic topology, these features are easier to understand for the compact subspace Hom(N,K) of Hom(N,G) where K is a maximal compact subgroup of G (e.g. a special unitary group). Unfortunately, the topological spaces Hom(N,G) and Hom(N,K) usually have very little to do with each other; for instance, some of the components of Hom(N,G) may not even intersect Hom(N,K). Accordingly, I will discuss exceptional classes of groups N for which Hom(N,G) and Hom(N,K) happen to be homotopy equivalent, thereby allowing one to obtain otherwise inaccessible topological invariants. Submitted by
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