# Cubulating one-relator products with torsion

## TL;DR

This paper extends the understanding of group actions on CAT(0) cube complexes by showing that certain one-relator products with torsion admit proper, cocompact actions, generalizing previous results to a broader class.

## Contribution

It generalizes prior work by Lauer and Wise, demonstrating that one-relator products with torsion and factors acting on CAT(0) cube complexes also admit such actions.

## Key findings

- One-relator products with relator exponent ≥ 4 act on CAT(0) cube complexes.
- The result applies to locally indicable groups.
- Proper and cocompact actions are established for these groups.

## Abstract

We generalize results of Lauer and Wise to show that a one-relator product of locally indicable groups whose defining relator has exponent at least 4 admits a proper and cocompact action on a CAT(0) cube complex if the factors do.