Zero-surgery characterizes infinitely many knots
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912224654655488 |
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| author | Baldwin, John A. Sivek, Steven |
| author_facet | Baldwin, John A. Sivek, Steven |
| contents | We prove that 0 is a characterizing slope for infinitely many knots, namely the genus-1 knots whose knot Floer homology is 2-dimensional in the top Alexander grading, which we classified in recent work and which include all $(-3,3,2n+1)$ pretzel knots. This was previously only known for $5_2$ and its mirror, as a corollary of that classification, and for the unknot, trefoils, and the figure eight by work of Gabai from 1987. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_04280 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Zero-surgery characterizes infinitely many knots Baldwin, John A. Sivek, Steven Geometric Topology We prove that 0 is a characterizing slope for infinitely many knots, namely the genus-1 knots whose knot Floer homology is 2-dimensional in the top Alexander grading, which we classified in recent work and which include all $(-3,3,2n+1)$ pretzel knots. This was previously only known for $5_2$ and its mirror, as a corollary of that classification, and for the unknot, trefoils, and the figure eight by work of Gabai from 1987. |
| title | Zero-surgery characterizes infinitely many knots |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2211.04280 |