The purely cosmetic surgery conjecture is true for the Kinoshita-Terasaka and Conway knot families

TL;DR

This paper proves that all nontrivial members of the Kinoshita-Terasaka and Conway knot families satisfy the purely cosmetic surgery conjecture, advancing understanding of knot theory and cosmetic surgeries.

Contribution

It establishes the conjecture for these specific knot families, providing new evidence supporting the conjecture's validity.

Findings

All nontrivial Kinoshita-Terasaka knots satisfy the conjecture.

All nontrivial Conway knots satisfy the conjecture.

Supports the broader validity of the purely cosmetic surgery conjecture.

Abstract

We show that all nontrivial members of the Kinoshita-Terasaka and Conway knot families satisfy the purely cosmetic surgery conjecture.