Non-integer characterizing slopes and knot Floer homology
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916605010640896 |
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| author | McCoy, Duncan |
| author_facet | McCoy, Duncan |
| contents | Conjecturally, a knot in the 3-sphere has only finitely many non-integer non-characterizing slopes. We verify this conjecture for all knots with knot Floer homology satisfying certain simplicity conditions. The class of knots satisfying our notion of simplicity includes alternating knots, $L$-space knots and the vast majority of knots with at most 12 crossings. For arbitrary knots in the 3-sphere we show that almost all slopes $p/q$ with $|q|\geq 3$ are characterizing. In addition, we show that all $L$-space knots and almost $L$-space knots have infinitely many integer characterizing slopes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01789 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-integer characterizing slopes and knot Floer homology McCoy, Duncan Geometric Topology Conjecturally, a knot in the 3-sphere has only finitely many non-integer non-characterizing slopes. We verify this conjecture for all knots with knot Floer homology satisfying certain simplicity conditions. The class of knots satisfying our notion of simplicity includes alternating knots, $L$-space knots and the vast majority of knots with at most 12 crossings. For arbitrary knots in the 3-sphere we show that almost all slopes $p/q$ with $|q|\geq 3$ are characterizing. In addition, we show that all $L$-space knots and almost $L$-space knots have infinitely many integer characterizing slopes. |
| title | Non-integer characterizing slopes and knot Floer homology |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2309.01789 |