Discrete subgroups of semisimple Lie groups, beyond lattices
| Autor: | Kassel, Fanny |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | Discrete subgroups of SL(2,R) are well understood, and classified by the geometry of the corresponding hyperbolic surfaces. Discrete subgroups of higher-rank semisimple Lie groups, such as SL(n,R) for n>2, remain more mysterious. While lattices in this setting are rigid, there also exist more flexible, "thinner" discrete subgroups, which may have large and interesting deformation spaces, giving rise in particular to so-called higher Teichm\"uller theory. We survey recent progress in constructing and understanding such discrete subgroups from a geometric and dynamical viewpoint. Comment: 73 pages, 11 figures. To appear in the Proceedings of Groups St Andrews 2022 in Newcastle, Cambridge University Press |
| Databáze: | arXiv |
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