A note on abelian cubulated groups

TL;DR

This paper discusses the property that abelian groups acting freely on CAT(0) cube complexes are necessarily free abelian, highlighting a specific structural aspect of such group actions.

Contribution

It establishes that any abelian group acting freely on a CAT(0) cube complex must be free abelian, providing insight into the structure of these group actions.

Findings

Abelian groups acting freely on CAT(0) cube complexes are free abelian.

The result clarifies the structure of group actions on CAT(0) cube complexes.

Supports the understanding of geometric group theory in non-positively curved spaces.

Abstract

An abelian group acting freely on a $\mathrm{CAT}(0)$ cube complex is free abelian.