Cubulating a free-product-by-cyclic group

2022/12/19 by François Dahmani, Dahmani, François, Suraj Krishna M S +1
Mathematics · #20E08 #20E36 #20F65 #20F67 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2212.09869

openalex publication_date 2022/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Let G = H₁ * ... * H_k * F_r be a torsion-free group and ϕ an automorphism of G that preserves this free factor system. We show that when ϕ is fully irreducible and atoroidal relative to this free factor system, the mapping torus Γ= G \rtimes_ϕ 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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