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Hyperbolic
hyperbolic-by-cyclic groups are cubulable
François Dahmani, Suraj Krishna Meda Satish and Jean Pierre Mutanguha |
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Geometry & Topology 29 (2025) 259–268
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DOI: 10.2140/gt.2025.29.259
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Abstract |
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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 -subgroups. |
Keywords
mapping torus, cubulation, CAT(0) cube complex, linear,
hyperbolic groups, atoroidal
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Mathematical Subject Classification
Primary: 20E08, 20E36, 20F65, 20F67
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References |
Publication
Received: 30 June 2023
Revised: 4 October 2023
Accepted: 3 November 2023
Published: 1 January 2025
Proposed: Ian Agol
Seconded: Mladen Bestvina, Dmitri Burago
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Authors |
| François Dahmani | |
| IRL CRM-CNRS Université de Montréal Montreal Canada |
Institut Fourier Laboratoire de Mathématiques, Université Grenoble Alpes Grenoble France |
| Suraj Krishna Meda Satish | |
| Department of Mathematics Ashoka University Haryana India |
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| Jean Pierre Mutanguha | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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