Zariski-dense surface groups in non-uniform lattices of split real Lie groups
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| Format: | Preprint |
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2022
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| _version_ | 1866915759975825408 |
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| author | Audibert, Jacques |
| author_facet | Audibert, Jacques |
| contents | For $\textrm{SL}(n,\mathbb{R})$ ($n\geq3$), $\textrm{SO}(n+1,n)$ ($n\geq2$), $\textrm{Sp}(2n,\mathbb{R})$ ($n\geq2$) and for the adjoint real split form of the exceptional group $\textrm{G}_2$, we exhibit non-uniform lattices in which we construct thin Hitchin representations by arithmetic methods. These representations give infinitely many orbits under the action of the mapping class group (except maybe for $\textrm{G}_2$). In particular, we show that when $p\neq2$ is prime every non-uniform lattice of $\mathrm{SL}(p,\mathbb{R})$ contains thin Hitchin representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_01123 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Zariski-dense surface groups in non-uniform lattices of split real Lie groups Audibert, Jacques Geometric Topology Group Theory Number Theory 22E40 For $\textrm{SL}(n,\mathbb{R})$ ($n\geq3$), $\textrm{SO}(n+1,n)$ ($n\geq2$), $\textrm{Sp}(2n,\mathbb{R})$ ($n\geq2$) and for the adjoint real split form of the exceptional group $\textrm{G}_2$, we exhibit non-uniform lattices in which we construct thin Hitchin representations by arithmetic methods. These representations give infinitely many orbits under the action of the mapping class group (except maybe for $\textrm{G}_2$). In particular, we show that when $p\neq2$ is prime every non-uniform lattice of $\mathrm{SL}(p,\mathbb{R})$ contains thin Hitchin representations. |
| title | Zariski-dense surface groups in non-uniform lattices of split real Lie groups |
| topic | Geometric Topology Group Theory Number Theory 22E40 |
| url | https://arxiv.org/abs/2206.01123 |