Profile: Thomas Hill ⟨thill@math.utah.edu⟩
Title: Automorphisms of the sphere complex of an infinite graph
Abstract:
For a locally finite, connected graph $\Gamma$, let
$\operatorname{Map}(\Gamma)$ denote the group of proper homotopy equivalences of
$\Gamma$ up to proper homotopy.
Excluding
sporadic cases, we show
$\operatorname{Aut}(\mathcal{S}(M_\Gamma)) \cong \operatorname{Map}(\Gamma)$, where $\mathcal{S}(M_\Gamma)$ is
the sphere complex of the doubled handlebody $M_\Gamma$ associated
to $\Gamma$. We also construct an exhaustion of $\mathcal{S}(M_\Gamma)$
by finite strongly rigid sets when $\Gamma$ has finite rank and
finitely many rays, and an
appropriate generalization otherwise. This is joint work with Michael Kopreski, Rebecca Rechkin, George
Shaji, and Brian Udall.
Notes: preprint: https://arxiv.org/abs/2410.06531
Status: Accepted
Collection: Geometric Group Theory