Duke Mathematical Journal

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

Mark F. Hagen and Daniel T. Wise

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Let V be a finite graph, and let ϕ:VV be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group G. Then G acts freely and cocompactly on a CAT(0) cube complex. Hence, if F is a finite-rank free group and if Φ:FF is an irreducible monomorphism so that G=FΦ is word-hyperbolic, then G acts freely and cocompactly on a CAT(0) cube complex. This holds, in particular, if Φ is an irreducible automorphism with G=FΦZ word-hyperbolic.

Article information

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

Received: 8 November 2013
Revised: 17 August 2015
First available in Project Euclid: 24 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 57M20: Two-dimensional complexes

free-by-cyclic group $\operatorname{CAT}(0)$ cube complex train track map train-track map


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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