Zero-surgery characterizes infinitely many knots

TL;DR

This paper proves that zero surgery uniquely determines infinitely many genus-1 knots with specific Floer homology properties, expanding the class of knots known to be characterized by their 0-surgery.

Contribution

It establishes that 0 is a characterizing slope for an infinite family of genus-1 knots with particular Floer homology, including all (-3,3,2n+1) pretzel knots, generalizing previous results.

Findings

0 is a characterizing slope for infinitely many genus-1 knots

Includes all (-3,3,2n+1) pretzel knots

Extends known characterizations beyond previously known knots

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.