Cubulating a free-product-by-cyclic group

Dahmani, François¹ ; Meda Satish, Suraj Krishna²

¹Institut Fourier, University Grenoble Alpes, Grenoble, France
²Department of Mathematics, Ashoka University, Haryana, India

Algebraic and Geometric Topology, Tome 25 (2025) no. 3, pp. 1561-1597

Résumé

Let G = H1 ∗⋯ ∗ Hk ∗ Fr be a finitely generated 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 ⋊ ϕℤ 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.

Détail

DOI : 10.2140/agt.2025.25.1561

Keywords: mapping torus, relative cubulation, CAT(0) cube complex, train track, relative hyperbolicity, atoroidal, fully irreducible

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