## Duke Mathematical Journal

### Cubulating hyperbolic free-by-cyclic groups: The irreducible case

#### Abstract

Let $V$ be a finite graph, and let $\phi:V\rightarrow V$ be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group $G$. Then $G$ acts freely and cocompactly on a $\operatorname{CAT}(0)$ cube complex. Hence, if $F$ is a finite-rank free group and if $\Phi:F\to F$ is an irreducible monomorphism so that $G=F*_{\Phi}$ is word-hyperbolic, then $G$ acts freely and cocompactly on a $\operatorname{CAT}(0)$ cube complex. This holds, in particular, if $\Phi$ is an irreducible automorphism with $G=F\rtimes_{\Phi}\mathbb{Z}$ word-hyperbolic.

#### Article information

Source
Duke Math. J., Volume 165, Number 9 (2016), 1753-1813.

Dates
Revised: 17 August 2015
First available in Project Euclid: 24 March 2016

https://projecteuclid.org/euclid.dmj/1458829437

Digital Object Identifier
doi:10.1215/00127094-3450752

Mathematical Reviews number (MathSciNet)
MR3320891

Zentralblatt MATH identifier
06603541

Subjects
Secondary: 57M20: Two-dimensional complexes

#### Citation

Hagen, Mark F.; Wise, Daniel T. Cubulating hyperbolic free-by-cyclic groups: The irreducible case. Duke Math. J. 165 (2016), no. 9, 1753--1813. doi:10.1215/00127094-3450752. https://projecteuclid.org/euclid.dmj/1458829437

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