## 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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