Rigidity of pseudo-free group actions on contractible manifolds

TL;DR

This paper studies the classification of certain group actions on contractible manifolds, extending previous work on involutions and including examples from Coxeter groups acting on CAT(0) spaces.

Contribution

It generalizes the classification of pseudo-free involutions on tori to broader group actions on contractible manifolds, incorporating non-Riemannian examples.

Findings

Extended classification of pseudo-free involutions on tori.

Constructed a non-Riemannian example from Coxeter group actions.

Analyzed the properties of group actions with torsion in universal covers.

Abstract

This article announces joint work with Frank Connolly and Jim Davis. We generalize our classification of pseudo-free involutions on the n-torus, by studying the action of the associated infinite group with torsion in the universal cover. Included is a non-Riemannian example obtained from the restriction of the action of a Coxeter group on a CAT(0) manifold.