# Geometric Analysis and Topology Seminar

#### Hyperbolic Out(F_N)-Complexes

Speaker: Mark Feighn, Rutgers Newark

Location: Warren Weaver Hall 202

Date: Friday, November 12, 2010, 11 a.m.

Synopsis:

Much current work in geometric group theory is motivated by analogues between the mapping class group $$MCG(S)$$ of a compact surface $$S$$ and the outer automorphism group $$Out(F_n)$$ of a rank $$n$$ free group $$F_n$$. On the $$MCG$$ side, there is the curve complex $$C(S)$$ and the celebrated result of Masur and Minsky that $$C(S)$$ is hyperbolic in the sense of Gromov. On the $$Out(F_n)$$ side, as yet there is no satisfying replacement for the curve complex. I will discuss joint work with Mladen Bestvina in which we construct some hyperbolic $$Out(F_n)$$-graphs that can serve as curve complex replacements for certain applications.