Tight contact structures on hyperbolic homology 3-spheres
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917677366247424 |
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| author | Mj, Mahan Sen, Balarka |
| author_facet | Mj, Mahan Sen, Balarka |
| contents | We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many distinct tight contact structures within the same homotopy class of oriented plane distributions. As a corollary, we give a recipe to construct hyperbolic L-spaces admitting arbitrarily many distinct tight contact structures. We also introduce a notion of geometric limits of contact structures compatible with geometric limits of hyperbolic manifolds and study the behavior of the tight contact structures we construct under geometric limits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14698 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tight contact structures on hyperbolic homology 3-spheres Mj, Mahan Sen, Balarka Geometric Topology Symplectic Geometry 57R17, 57M50 We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many distinct tight contact structures within the same homotopy class of oriented plane distributions. As a corollary, we give a recipe to construct hyperbolic L-spaces admitting arbitrarily many distinct tight contact structures. We also introduce a notion of geometric limits of contact structures compatible with geometric limits of hyperbolic manifolds and study the behavior of the tight contact structures we construct under geometric limits. |
| title | Tight contact structures on hyperbolic homology 3-spheres |
| topic | Geometric Topology Symplectic Geometry 57R17, 57M50 |
| url | https://arxiv.org/abs/2404.14698 |