Ping-pong in Hadamard manifolds
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2018
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| _version_ | 1866914650903281664 |
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| author | Dey, Subhadip Kapovich, Michael Liu, Beibei |
| author_facet | Dey, Subhadip Kapovich, Michael Liu, Beibei |
| contents | In this paper, we prove a quantitative version of the Tits alternative for negatively pinched manifolds $X$. Precisely, we prove that a nonelementary discrete isometry subgroup of $\mathrm{Isom}(X)$ generated by two non-elliptic isometries $g$, $f$ contains a free subgroup of rank $2$ generated by isometries $f^N , h$ of uniformly bounded word length. Furthermore, we show that this free subgroup is convex-cocompact when $f$ is hyperbolic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1806_07020 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Ping-pong in Hadamard manifolds Dey, Subhadip Kapovich, Michael Liu, Beibei Group Theory Differential Geometry Geometric Topology 20F65, 22E40, 53C20, 57N16 In this paper, we prove a quantitative version of the Tits alternative for negatively pinched manifolds $X$. Precisely, we prove that a nonelementary discrete isometry subgroup of $\mathrm{Isom}(X)$ generated by two non-elliptic isometries $g$, $f$ contains a free subgroup of rank $2$ generated by isometries $f^N , h$ of uniformly bounded word length. Furthermore, we show that this free subgroup is convex-cocompact when $f$ is hyperbolic. |
| title | Ping-pong in Hadamard manifolds |
| topic | Group Theory Differential Geometry Geometric Topology 20F65, 22E40, 53C20, 57N16 |
| url | https://arxiv.org/abs/1806.07020 |