Avatars of Margulis invariants and proper actions
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arXiv
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| Format: | Preprint |
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2018
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| _version_ | 1866916539098202112 |
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| author | Ghosh, Sourav |
| author_facet | Ghosh, Sourav |
| contents | In this article, we provide a necessary and sufficient criterion for proper actions on $\mathbb{H}^{n,n-1}$ in terms of certain special Anosov representations in $\mathsf{SO}(n,n)$. Moreover, we show that affine Anosov representations of any word hyperbolic group in $\mathsf{SO}(n,n-1)\ltimes\mathbb{R}^{2n-1}$ are infinitesimal versions of such special Anosov representations. Finally, using the above two results we interpret Margulis spacetimes as infinitesimal versions of quotient manifolds of $\mathbb{H}^{n,n-1}$.
In the appendix, we give a description of the appropriate cross-ratios in our setting and their infinitesimal versions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1812_03777 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Avatars of Margulis invariants and proper actions Ghosh, Sourav Geometric Topology Differential Geometry Dynamical Systems 53-xx, 37-xx In this article, we provide a necessary and sufficient criterion for proper actions on $\mathbb{H}^{n,n-1}$ in terms of certain special Anosov representations in $\mathsf{SO}(n,n)$. Moreover, we show that affine Anosov representations of any word hyperbolic group in $\mathsf{SO}(n,n-1)\ltimes\mathbb{R}^{2n-1}$ are infinitesimal versions of such special Anosov representations. Finally, using the above two results we interpret Margulis spacetimes as infinitesimal versions of quotient manifolds of $\mathbb{H}^{n,n-1}$. In the appendix, we give a description of the appropriate cross-ratios in our setting and their infinitesimal versions. |
| title | Avatars of Margulis invariants and proper actions |
| topic | Geometric Topology Differential Geometry Dynamical Systems 53-xx, 37-xx |
| url | https://arxiv.org/abs/1812.03777 |