Controlling manifold covers of orbifolds

TL;DR

This paper generalizes Selberg's lemma to orbifold covers, providing new methods to find torsion-free subgroups of arithmetic groups with applications in geometry and resolving longstanding conjectures.

Contribution

It extends Selberg's lemma to manifold covers of orbifolds, offering novel techniques and resolving open questions in geometric group theory.

Findings

Established existence of torsion-free, finite index subgroups for orbifold groups

Resolved a conjecture of Nimershiem in geometric topology

Answered questions posed by Long-Reid and the author

Abstract

In this article we prove a generalization of Selberg's lemma on the existence of torsion free, finite index subgroups of arithmetic groups. Some of the geometric applications are the resolution a conjecture of Nimershiem and answers to questions of Long-Reid and the author.