Effective hyperbolization and length bounds for Heegaard splittings
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914911528943616 |
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| author | Feller, Peter Sisto, Alessandro Viaggi, Gabriele |
| author_facet | Feller, Peter Sisto, Alessandro Viaggi, Gabriele |
| contents | We consider 3-manifolds given as Heegaard splittings $M=H^-\cup_ΣH^+$ with the aim to describe the hyperbolic metric of $M$ under topological conditions on the splitting guaranteeing that the manifold is hyperbolic. In particular, given a suitable "sufficiently incompressible" curve $γ\subsetΣ$, we show (without appealing to Geometrization) that $M$ is hyperbolic and we compute the length of $γ$ in terms of the projection coefficients of the disk sets, up to a uniform multiplicative error. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06998 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effective hyperbolization and length bounds for Heegaard splittings Feller, Peter Sisto, Alessandro Viaggi, Gabriele Geometric Topology 57K32, 57K20 We consider 3-manifolds given as Heegaard splittings $M=H^-\cup_ΣH^+$ with the aim to describe the hyperbolic metric of $M$ under topological conditions on the splitting guaranteeing that the manifold is hyperbolic. In particular, given a suitable "sufficiently incompressible" curve $γ\subsetΣ$, we show (without appealing to Geometrization) that $M$ is hyperbolic and we compute the length of $γ$ in terms of the projection coefficients of the disk sets, up to a uniform multiplicative error. |
| title | Effective hyperbolization and length bounds for Heegaard splittings |
| topic | Geometric Topology 57K32, 57K20 |
| url | https://arxiv.org/abs/2408.06998 |