Nonexistence and existence of fillable contact structures on 3-manifolds
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866929729392607232 |
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| author | Ding, Fan Li, Youlin Wu, Zhongtao |
| author_facet | Ding, Fan Li, Youlin Wu, Zhongtao |
| contents | In the first part of this paper, we construct infinitely many hyperbolic closed 3-manifolds which admit no symplectic fillable contact structure. All these 3-manifolds are obtained by Dehn surgeries along L-space knots or L-space two-component links. In the second part of this paper, we show that Dehn surgeries along certain knots and links, including those considered in the first part, admit Stein fillable contact structures as long as the surgery coefficients are sufficiently large. This provides some new evidence for the high surgery conjecture raised by Stipsicz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_02151 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Nonexistence and existence of fillable contact structures on 3-manifolds Ding, Fan Li, Youlin Wu, Zhongtao Geometric Topology Symplectic Geometry In the first part of this paper, we construct infinitely many hyperbolic closed 3-manifolds which admit no symplectic fillable contact structure. All these 3-manifolds are obtained by Dehn surgeries along L-space knots or L-space two-component links. In the second part of this paper, we show that Dehn surgeries along certain knots and links, including those considered in the first part, admit Stein fillable contact structures as long as the surgery coefficients are sufficiently large. This provides some new evidence for the high surgery conjecture raised by Stipsicz. |
| title | Nonexistence and existence of fillable contact structures on 3-manifolds |
| topic | Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2111.02151 |