Simply transitive geodesics and omnipotence of lattices in PSL$(2,\mathbb{C})$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| author | Agol, Ian Cheetham-West, Tam Minsky, Yair |
| author_facet | Agol, Ian Cheetham-West, Tam Minsky, Yair |
| contents | We show that the isometry group of a finite-volume hyperbolic 3-manifold acts simply transitively on many of its closed geodesics. Combining this observation with the Virtual Special Theorems of the first author and Wise, we show that every non-arithmetic lattice in PSL$(2,\mathbb{C})$ is the full group of orientation-preserving isometries for some other lattice and that the orientation-preserving isometry group of a finite-volume hyperbolic 3-manifold acts non-trivially on the homology of some finite-sheeted cover. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08418 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simply transitive geodesics and omnipotence of lattices in PSL$(2,\mathbb{C})$ Agol, Ian Cheetham-West, Tam Minsky, Yair Geometric Topology Group Theory 57K32 We show that the isometry group of a finite-volume hyperbolic 3-manifold acts simply transitively on many of its closed geodesics. Combining this observation with the Virtual Special Theorems of the first author and Wise, we show that every non-arithmetic lattice in PSL$(2,\mathbb{C})$ is the full group of orientation-preserving isometries for some other lattice and that the orientation-preserving isometry group of a finite-volume hyperbolic 3-manifold acts non-trivially on the homology of some finite-sheeted cover. |
| title | Simply transitive geodesics and omnipotence of lattices in PSL$(2,\mathbb{C})$ |
| topic | Geometric Topology Group Theory 57K32 |
| url | https://arxiv.org/abs/2409.08418 |