Tuesday, April 6William Thurston, Cornell University
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.Back to seminar home page.