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arXiv · 2212.09869

Cubulating a free-product-by-cyclic group

François Dahmani·Suraj Krishna M S
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Abstract

Let $G = H_1 * ... * H_k * F_r$ be a torsion-free group and $\phi$ an automorphism of $G$ that preserves this free factor system. We show that when $\phi$ is fully irreducible and atoroidal relative to this free factor system, the mapping torus $\Gamma = G \rtimes_{\phi} \mathbb{Z}$ 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.

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François Dahmani, Suraj Krishna M S. 2022-12-19. Cubulating a free-product-by-cyclic group. https://doi.org/10.2140/agt.2025.25.1561

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