Proper affine deformations of positive representations
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914807979966464 |
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| author | Burelle, Jean-Philippe Korenjak, Neža Žager |
| author_facet | Burelle, Jean-Philippe Korenjak, Neža Žager |
| contents | We define for every positive Anosov representation of a nonabelian free group into $\mathrm{SO}(2n,2n-1)$ a family of $\mathbb{R}^{4n-1}$-valued cocycles which induce proper affine actions on $\mathbb{R}^{4n-1}$. We construct fundamental domains in $\mathbb{R}^{4n-1}$ bounded by generalized crooked planes for these affine actions, and deduce that the quotient manifolds are homeomorphic to handlebodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14658 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proper affine deformations of positive representations Burelle, Jean-Philippe Korenjak, Neža Žager Differential Geometry Geometric Topology 22E40, 20H10 We define for every positive Anosov representation of a nonabelian free group into $\mathrm{SO}(2n,2n-1)$ a family of $\mathbb{R}^{4n-1}$-valued cocycles which induce proper affine actions on $\mathbb{R}^{4n-1}$. We construct fundamental domains in $\mathbb{R}^{4n-1}$ bounded by generalized crooked planes for these affine actions, and deduce that the quotient manifolds are homeomorphic to handlebodies. |
| title | Proper affine deformations of positive representations |
| topic | Differential Geometry Geometric Topology 22E40, 20H10 |
| url | https://arxiv.org/abs/2405.14658 |