Cubulating hyperbolic free-by-cyclic groups: the general case

TL;DR

This paper proves that hyperbolic free-by-cyclic groups act freely and cocompactly on CAT(0) cube complexes, extending cubulation results to the general case.

Contribution

It establishes the cubulation of all hyperbolic free-by-cyclic groups, generalizing previous results to the broader class.

Findings

Hyperbolic free-by-cyclic groups act on CAT(0) cube complexes

The action is free and cocompact

Extends cubulation to the general case

Abstract

Let $\Phi:F\rightarrow F$ be an automorphism of the finite-rank free group $F$. Suppose that $G=F\rtimes_\Phi\mathbb Z$ is word-hyperbolic. Then $G$ acts freely and cocompactly on a CAT(0) cube complex.