Cubulating a free-product-by-cyclic group

Abstract

Let $G=H_1\ast ...\ast H_k\ast F_r$ be a torsion-free group and $\varphi$ an automorphism of $G$ that preserves this free factor system. We show that when $\varphi$ is fully irreducible and atoroidal relative to this free factor system, the mapping torus $\Gamma =G{⋊}_{\varphi }\mathbb{Z}$ acts relatively geometrically on a hyperbolic CAT(0) cube complex. This is a generalisation of a result of Hagen and Wise for hyperbolic free-by-cyclic groups.

arXiv comment10 figures, incorporated referee suggestions. Final version, to appear in Alg. Geom. Topol

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