Primitive stability and the Q-conditions for the rank two free group in hyperbolic d-space
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911466516381696 |
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| author | Fléchelles, Balthazar |
| author_facet | Fléchelles, Balthazar |
| contents | The two largest known domains of discontinuity for the action of Out(F_2) on the PSL(2,C)-character variety of F_2 - defined by Minsky's primitive stability, and Bowditch's Q-conditions - were proven to be equal independently by Lee-Xu and Series. We prove the equivalence between primitive stability and a generalization of the Q-conditions for representations of F_2 into the isometry group of hyperbolic d-space for d >= 3, under some assumptions. In particular, these assumptions are satisfied by all W_3-extensible representations.
We also generalize Lee-Xu's and Series' results concerning the bounded intersection property to higher dimensions after extending their original definition to this setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09771 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Primitive stability and the Q-conditions for the rank two free group in hyperbolic d-space Fléchelles, Balthazar Geometric Topology 14M35, 51M10, 20E05, 20E36 The two largest known domains of discontinuity for the action of Out(F_2) on the PSL(2,C)-character variety of F_2 - defined by Minsky's primitive stability, and Bowditch's Q-conditions - were proven to be equal independently by Lee-Xu and Series. We prove the equivalence between primitive stability and a generalization of the Q-conditions for representations of F_2 into the isometry group of hyperbolic d-space for d >= 3, under some assumptions. In particular, these assumptions are satisfied by all W_3-extensible representations. We also generalize Lee-Xu's and Series' results concerning the bounded intersection property to higher dimensions after extending their original definition to this setting. |
| title | Primitive stability and the Q-conditions for the rank two free group in hyperbolic d-space |
| topic | Geometric Topology 14M35, 51M10, 20E05, 20E36 |
| url | https://arxiv.org/abs/2507.09771 |