Discrete group actions on 3-manifolds and embeddable Cayley complexes

Abstract

We prove that a group $\Gamma$ admits a discrete topological (equivalently, smooth) action on some simply-connected 3-manifold if and only if $\Gamma$ has a Cayley complex embeddable -- with certain natural restrictions -- in one of the following four 3-manifolds: (i) ${\mathbb{S}}^3$, (ii) ${\mathbb{R}}^3$, (iii) ${\mathbb{S}}^2\times \mathbb{R}$, (iv) the complement of a tame Cantor set in ${\mathbb{S}}^3$.

References in corpus (2)

• Smoothing finite group actions on three-manifolds
• Contractible open manifolds which embed in no compact, locally connected and locally 1-connected metric space