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Cubulated hyperbolic
groups admit Anosov representations
Sami Douba, Balthazar Fléchelles, Theodore Weisman and Feng Zhu |
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Geometry & Topology 29 (2025) 4695–4766
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DOI: 10.2140/gt.2025.29.4695
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Abstract |
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We prove that any hyperbolic group acting properly discontinuously and cocompactly on a cube complex admits a projective Anosov representation into for some . More specifically, we show that if is a hyperbolic quasiconvex subgroup of a right-angled Coxeter group , then a generic representation of by reflections restricts to a projective Anosov representation of . |
Keywords
discrete subgroups of Lie groups, geometric group theory,
Anosov representations, Coxeter groups, hyperbolic groups
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Mathematical Subject Classification
Primary: 22E40
Secondary: 20F55, 20F67
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References |
Publication
Received: 17 November 2023
Revised: 26 September 2024
Accepted: 25 January 2025
Published: 31 December 2025
Proposed: Ian Agol
Seconded: Mladen Bestvina, Anna Wienhard
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Authors |
| Sami Douba | |
| Institut des Hautes Études
Scientifiques Bures-sur-Yvette France |
Mathematisches Institut der
Universität Bonn Bonn Germany |
| Balthazar Fléchelles | |
| Institut des Hautes Études
Scientifiques Bures-sur-Yvette France |
Université Grenoble-Alpes, Institut
Fourier Gières France |
| Theodore Weisman | |
| Department of Mathematics University of Michigan Ann Arbor, MI United States |
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| Feng Zhu | |
| Department of Mathematics University of Wisconsin, Madison Madison, WI United States |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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