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arXiv · 2211.04280

Zero-surgery characterizes infinitely many knots

John A. Baldwin·Steven Sivek
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Abstract

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.

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John A. Baldwin, Steven Sivek. 2023-10-16. Zero-surgery characterizes infinitely many knots. https://doi.org/10.4310/mrl.250210230206

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