Rational approximation for Hitchin representations
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908286201102336 |
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| author | Audibert, Jacques Zshornack, Michael |
| author_facet | Audibert, Jacques Zshornack, Michael |
| contents | A consequence of Rapinchuk et al. is that for $S$ a closed surface of genus $g\geq 2$, the set of Hitchin representations of $π_1(S)$ with image in $\mathrm{SL}(n,\mathbb{Q})$ is dense in the Hitchin component. We give a dynamical proof of this fact provided that $g\geq 3$. Moreover, we extend it to some other $\mathbb{Q}$-groups such as $\mathrm{Sp}(2k,\mathbb{Q})$ and $\mathrm{G}_2(\mathbb{Q})$, where the results are new. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_15121 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rational approximation for Hitchin representations Audibert, Jacques Zshornack, Michael Geometric Topology Group Theory 22E40 A consequence of Rapinchuk et al. is that for $S$ a closed surface of genus $g\geq 2$, the set of Hitchin representations of $π_1(S)$ with image in $\mathrm{SL}(n,\mathbb{Q})$ is dense in the Hitchin component. We give a dynamical proof of this fact provided that $g\geq 3$. Moreover, we extend it to some other $\mathbb{Q}$-groups such as $\mathrm{Sp}(2k,\mathbb{Q})$ and $\mathrm{G}_2(\mathbb{Q})$, where the results are new. |
| title | Rational approximation for Hitchin representations |
| topic | Geometric Topology Group Theory 22E40 |
| url | https://arxiv.org/abs/2310.15121 |