Topology & Geometric Group Theory Seminar

Spring 2010

1:30 – 2:30, Malott 203

Tuesday, April 6

William Thurston, Cornell University

Approximately finite groups

There is a compact topological space consisting of all k-generated (i.e., marked) groups. A k-generated group is approximately finite if it is a limit point of finite groups. I will discuss this picture, and use it to show that for any N, there are (many) word-hyperbolic groups with no non-trivial homomorphisms to GL(N, any field). Heuristics suggest that typical word-hyperbolic groups with several more relators than generators should have no finite quotients at all.

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