# 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.