Which reducible representations are Anosov?
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916493077250048 |
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| author | Lahn, Max |
| author_facet | Lahn, Max |
| contents | We give a characterization of the Anosov condition for reducible representations in terms of the eigenvalue magnitudes of the irreducible block factors of its block diagonalization. As in previous work, these Anosov representations comprise a collection of bounded convex domains in a finite-dimensional vector space, and this perspective allows us to conclude for many non-elementary hyperbolic groups that connected components of the character variety which consist entirely of Anosov representations do not contain reducible representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15321 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Which reducible representations are Anosov? Lahn, Max Group Theory Geometric Topology 22E40 (Primary) 20H10, 20H20 (Secondary) We give a characterization of the Anosov condition for reducible representations in terms of the eigenvalue magnitudes of the irreducible block factors of its block diagonalization. As in previous work, these Anosov representations comprise a collection of bounded convex domains in a finite-dimensional vector space, and this perspective allows us to conclude for many non-elementary hyperbolic groups that connected components of the character variety which consist entirely of Anosov representations do not contain reducible representations. |
| title | Which reducible representations are Anosov? |
| topic | Group Theory Geometric Topology 22E40 (Primary) 20H10, 20H20 (Secondary) |
| url | https://arxiv.org/abs/2411.15321 |