Equivalence of primitive-stable and Bowditch actions of the free group of rank two on Gromov-hyperbolic spaces
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912160865583104 |
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| author | Schlich, Suzanne |
| author_facet | Schlich, Suzanne |
| contents | We prove that the set of Bowditch representations (introduced by Bowditch in 1998, then generalized by Tan, Wong and Zhang in 2008) and the set of primitive-stable representations (introduced by Minsky in 2013) of the free group of rank two in the isometry group of a Gromov-hyperbolic space are equal. The case of $\mathrm{PSL}(2,\mathbb{C})$-representations has already been proved by Lee and Xu and independently Series. Our proof in this context is independent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_14546 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Equivalence of primitive-stable and Bowditch actions of the free group of rank two on Gromov-hyperbolic spaces Schlich, Suzanne Geometric Topology 57M60, 30L05 (Primary) 20E05, 51F30 (Secondary) We prove that the set of Bowditch representations (introduced by Bowditch in 1998, then generalized by Tan, Wong and Zhang in 2008) and the set of primitive-stable representations (introduced by Minsky in 2013) of the free group of rank two in the isometry group of a Gromov-hyperbolic space are equal. The case of $\mathrm{PSL}(2,\mathbb{C})$-representations has already been proved by Lee and Xu and independently Series. Our proof in this context is independent. |
| title | Equivalence of primitive-stable and Bowditch actions of the free group of rank two on Gromov-hyperbolic spaces |
| topic | Geometric Topology 57M60, 30L05 (Primary) 20E05, 51F30 (Secondary) |
| url | https://arxiv.org/abs/2211.14546 |