Effective length-projection bounds for hyperbolic 3-manifolds diffeomorphic to $S\times\mathbb{R}$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909571800367104 |
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| author | Viaggi, Gabriele |
| author_facet | Viaggi, Gabriele |
| contents | We give a formula with explicit constants relating the subsurface projection $d_Y(ν^-,ν^+)$ of the end invariants $ν^-,ν^+$ of a hyperbolic 3-manifold $Q$ diffeomorphic to $S\times\mathbb{R}$ and the length of the geodesic representative in $Q$ of the multicurve $\partial Y$. This makes effective and computable the large projections versus short curves relation proved by Minsky. We give an application to closed hyperbolic 3-manifolds fibering over the circle providing a geometric analog of the uniform projection bound in fibered faces of Minsky and Taylor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06097 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective length-projection bounds for hyperbolic 3-manifolds diffeomorphic to $S\times\mathbb{R}$ Viaggi, Gabriele Geometric Topology Differential Geometry 57K32, 57K20 We give a formula with explicit constants relating the subsurface projection $d_Y(ν^-,ν^+)$ of the end invariants $ν^-,ν^+$ of a hyperbolic 3-manifold $Q$ diffeomorphic to $S\times\mathbb{R}$ and the length of the geodesic representative in $Q$ of the multicurve $\partial Y$. This makes effective and computable the large projections versus short curves relation proved by Minsky. We give an application to closed hyperbolic 3-manifolds fibering over the circle providing a geometric analog of the uniform projection bound in fibered faces of Minsky and Taylor. |
| title | Effective length-projection bounds for hyperbolic 3-manifolds diffeomorphic to $S\times\mathbb{R}$ |
| topic | Geometric Topology Differential Geometry 57K32, 57K20 |
| url | https://arxiv.org/abs/2504.06097 |