Neighborhoods of transverse knots and destabilizations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915978492772352 |
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| author | Etnyre, John B. |
| author_facet | Etnyre, John B. |
| contents | In this note, we show that transverse knots have unique standard neighborhoods and prove a structure theorem about non-loose Legendrian knots. We also prove a finiteness result for transverse knots in a tight contact manifold. The common theme of these two results is a general destabilization result for Legendrian knots. As a byproduct of this work, we find a manifold with an infinite number of distinct tight contact structures, up to contactomoprhism, with no Giroux torsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15651 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Neighborhoods of transverse knots and destabilizations Etnyre, John B. Geometric Topology Symplectic Geometry In this note, we show that transverse knots have unique standard neighborhoods and prove a structure theorem about non-loose Legendrian knots. We also prove a finiteness result for transverse knots in a tight contact manifold. The common theme of these two results is a general destabilization result for Legendrian knots. As a byproduct of this work, we find a manifold with an infinite number of distinct tight contact structures, up to contactomoprhism, with no Giroux torsion. |
| title | Neighborhoods of transverse knots and destabilizations |
| topic | Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2512.15651 |