Dehn filling in semisimple Lie groups
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929729955692544 |
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| author | Weisman, Theodore |
| author_facet | Weisman, Theodore |
| contents | We generalize one part of Thurston's hyperbolic Dehn filling theorem to arbitrary-rank semisimple Lie groups by showing that certain deformations of extended geometrically finite subgroups of a semisimple Lie group are still extended geometrically finite. As a special case, our theorem gives a criterion which guarantees that a deformation of a relatively Anosov subgroup is (non-relatively) Anosov, and also ensures that limit sets vary continuously. Our result also applies to several higher-rank examples in convex projective geometry which are outside of the relatively Anosov setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17592 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dehn filling in semisimple Lie groups Weisman, Theodore Geometric Topology Group Theory We generalize one part of Thurston's hyperbolic Dehn filling theorem to arbitrary-rank semisimple Lie groups by showing that certain deformations of extended geometrically finite subgroups of a semisimple Lie group are still extended geometrically finite. As a special case, our theorem gives a criterion which guarantees that a deformation of a relatively Anosov subgroup is (non-relatively) Anosov, and also ensures that limit sets vary continuously. Our result also applies to several higher-rank examples in convex projective geometry which are outside of the relatively Anosov setting. |
| title | Dehn filling in semisimple Lie groups |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2502.17592 |