Maximal representations in lattices of the symplectic group
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917923644243968 |
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| author | Audibert, Jacques |
| author_facet | Audibert, Jacques |
| contents | We prove that all lattices of Sp(2n,R), except those commensurable with Sp(4k+2,Z) when n=2k+1, contain the image of infinitely many mapping class group orbits of Zariski-dense maximal representation that are continuous deformations of maximal diagonal representations. In particular, we show that Sp(4k,Z) contain Zariski-dense surface subgroups for all k. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_06791 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maximal representations in lattices of the symplectic group Audibert, Jacques Geometric Topology Group Theory Number Theory 22E40 We prove that all lattices of Sp(2n,R), except those commensurable with Sp(4k+2,Z) when n=2k+1, contain the image of infinitely many mapping class group orbits of Zariski-dense maximal representation that are continuous deformations of maximal diagonal representations. In particular, we show that Sp(4k,Z) contain Zariski-dense surface subgroups for all k. |
| title | Maximal representations in lattices of the symplectic group |
| topic | Geometric Topology Group Theory Number Theory 22E40 |
| url | https://arxiv.org/abs/2307.06791 |