Hyperbolic hyperbolic-by-cyclic groups are cubulable

Dahmani, François¹ ; Meda Satish, Suraj Krishna² ; Mutanguha, Jean Pierre³

¹ IRL CRM-CNRS, Université de Montréal, Montreal, Canada, Institut Fourier, Laboratoire de Mathématiques, Université Grenoble Alpes, Grenoble, France
² Department of Mathematics, Ashoka University, Haryana, India
³ Department of Mathematics, Princeton University, Princeton, NJ, United States

Geometry & topology, Tome 29 (2025) no. 1, pp. 259-268.

Résumé

We show that the mapping torus of a hyperbolic group by a hyperbolic automorphism is cubulable. Along the way, we give an alternate proof of Hagen and Wise’s theorem that hyperbolic free-by-cyclic groups are cubulable, and extend to the case with torsion Brinkmann’s thesis that a torsion-free hyperbolic-by-cyclic group is hyperbolic if and only if it does not contain ${\mathbb{Z}}^2$-subgroups.

Détail

DOI : 10.2140/gt.2025.29.259

Keywords: mapping torus, cubulation, CAT(0) cube complex, linear, hyperbolic groups, atoroidal

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