Characterizing slopes for $5_2$

TL;DR

This paper proves that all rational slopes are characterizing for the knot 5_2, except possibly positive integers, and classifies certain Dehn surgeries related to Brieskorn spheres and L-spaces.

Contribution

It establishes the characterization of the 5_2 knot by all rational slopes, advancing understanding of Dehn surgeries and L-space knots.

Findings

All rational slopes are characterizing for 5_2, except possibly positive integers.

Classified Dehn surgeries on knots yielding the Brieskorn sphere Σ(2,3,11).

Studied knots with large integral surgeries that are almost L-spaces.

Abstract

We prove that all rational slopes are characterizing for the knot $5_2$, except possibly for positive integers. Along the way, we classify the Dehn surgeries on knots in $S^3$ that produce the Brieskorn sphere $\Sigma(2,3,11)$, and we study knots on which large integral surgeries are almost L-spaces.