Cubical accessibility and bounds on curves on surfaces

TL;DR

This paper establishes bounds on the size of cubulations of finitely presented groups and applies these bounds to derive results on acylindrical actions on CAT(0) cube complexes and on curves on surfaces.

Contribution

It introduces new bounds on cubulations of groups and applies them to improve understanding of group actions on cube complexes and surface curves.

Findings

Bound on size of d-dimensional cubulations of finitely presented groups

Acylindrical accessibility for actions on CAT(0) cube complexes

Bounds on curves on surfaces

Abstract

We bound the size of $d$-dimensional cubulations of finitely presented groups. We apply this bound to obtain acylindrical accessibility for actions on CAT(0) cube complexes and bounds on curves on surfaces.