Non-integer characterizing slopes and knot Floer homology

Duncan McCoy

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arXiv · 2309.01789

Non-integer characterizing slopes and knot Floer homology

Duncan McCoy

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Abstract

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.

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BibTeX RIS

Duncan McCoy. 2023-09-04. Non-integer characterizing slopes and knot Floer homology. https://arxiv.org/abs/2309.01789

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