Bi-Lipschitz rigidity of discrete subgroups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916242660524032 |
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| author | Canary, Richard Oh, Hee Zimmer, Andrew |
| author_facet | Canary, Richard Oh, Hee Zimmer, Andrew |
| contents | We obtain a bi-Lipschitz rigidity theorem for a Zariski dense discrete subgroup of a connected simple real algebraic group. As an application, we show that any Zariski dense discrete subgroup of a higher rank semisimple algebraic group $G$ cannot have a $C^1$-smooth slim limit set in $G/P$ for any non-maximal parabolic subgroup $P$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00249 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bi-Lipschitz rigidity of discrete subgroups Canary, Richard Oh, Hee Zimmer, Andrew Group Theory Dynamical Systems Geometric Topology We obtain a bi-Lipschitz rigidity theorem for a Zariski dense discrete subgroup of a connected simple real algebraic group. As an application, we show that any Zariski dense discrete subgroup of a higher rank semisimple algebraic group $G$ cannot have a $C^1$-smooth slim limit set in $G/P$ for any non-maximal parabolic subgroup $P$. |
| title | Bi-Lipschitz rigidity of discrete subgroups |
| topic | Group Theory Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2405.00249 |