Cubulated hyperbolic groups admit Anosov representations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912858458030080 |
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| author | Douba, Sami Fléchelles, Balthazar Weisman, Theodore Zhu, Feng |
| author_facet | Douba, Sami Fléchelles, Balthazar Weisman, Theodore Zhu, Feng |
| contents | We prove that any hyperbolic group acting properly discontinuously and cocompactly on a $\mathrm{CAT}(0)$ cube complex admits a projective Anosov representation into $\mathrm{SL}(d, \mathbb{R})$ for some $d$. More specifically, we show that if $Γ$ is a hyperbolic quasiconvex subgroup of a right-angled Coxeter group $C$, then a generic representation of $C$ by reflections restricts to a projective Anosov representation of $Γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03695 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cubulated hyperbolic groups admit Anosov representations Douba, Sami Fléchelles, Balthazar Weisman, Theodore Zhu, Feng Group Theory Geometric Topology We prove that any hyperbolic group acting properly discontinuously and cocompactly on a $\mathrm{CAT}(0)$ cube complex admits a projective Anosov representation into $\mathrm{SL}(d, \mathbb{R})$ for some $d$. More specifically, we show that if $Γ$ is a hyperbolic quasiconvex subgroup of a right-angled Coxeter group $C$, then a generic representation of $C$ by reflections restricts to a projective Anosov representation of $Γ$. |
| title | Cubulated hyperbolic groups admit Anosov representations |
| topic | Group Theory Geometric Topology |
| url | https://arxiv.org/abs/2309.03695 |