Geometry, Topology and Dynamics Seminar
Patrick Reynolds
University of Utah
The Gromov boundary of the complex of free factors
Abstract: The complex of free factors $\mathcal{F}_N$ for the rank-$N$ free
group $F_N$ is an analogue for the complex of curves for a surface. The
space $\mathcal{F}_N$ is a simplicial complex and is given the simplicial
metric; Bestvina and Feighn have shown that for $N>2$, $\mathcal{F}_N$ is
Gromov hyperbolic, giving an analogue of a celebrated theorem of Masur and
Minsky, stating that the complex of curves for a surface is hyperbolic
(except in a few exceptional cases). The point of this talk is to give a
description of the Gromov boundary $\partial \mathcal{F}$ of $\mathcal{F}$;
our description of $\partial \mathcal{F}$ is analogous to E. Klarreich's
description of the boundary of the complex of curves. We will also
discuss other "curve complexes for the free group" and their relation to
$\mathcal{F}$. This is work with Mladen Bestvina.
Wednesday October 10, 2012 at 3:00 PM in SEO 636