Affine Anosov representations and proper actions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866911764964179968 |
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| author | Ghosh, Sourav Treib, Nicolaus |
| author_facet | Ghosh, Sourav Treib, Nicolaus |
| contents | We define the notion of affine Anosov representations of word hyperbolic groups into the affine group $\mathsf{SO}^0(n+1,n)\ltimes\mathbb{R}^{2n+1}$. We then show that a representation $ρ$ of a word hyperbolic group is affine Anosov if and only if its linear part $\mathtt{L}_ρ$ is Anosov in $\mathsf{SO}^0(n+1,n)$ with respect to the stabilizer of a maximal isotropic plane and $ρ(Γ)$ acts properly on $\mathbb{R}^{2n+1}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1711_09712 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Affine Anosov representations and proper actions Ghosh, Sourav Treib, Nicolaus Geometric Topology Differential Geometry We define the notion of affine Anosov representations of word hyperbolic groups into the affine group $\mathsf{SO}^0(n+1,n)\ltimes\mathbb{R}^{2n+1}$. We then show that a representation $ρ$ of a word hyperbolic group is affine Anosov if and only if its linear part $\mathtt{L}_ρ$ is Anosov in $\mathsf{SO}^0(n+1,n)$ with respect to the stabilizer of a maximal isotropic plane and $ρ(Γ)$ acts properly on $\mathbb{R}^{2n+1}$. |
| title | Affine Anosov representations and proper actions |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/1711.09712 |