Thurston norm and cosmetic surgeries

TL;DR

This paper investigates the conditions under which cosmetic surgeries on knots produce homeomorphic manifolds, showing that under certain Thurston norm conditions, the surgery coefficients must be equal up to sign.

Contribution

It establishes a new criterion linking the Thurston norm to the uniqueness of cosmetic surgeries on null-homologous knots.

Findings

Cosmetic surgeries imply equal or sign-related surgery coefficients under specific Thurston norm conditions.

The result constrains the possible pairs of cosmetic surgeries for certain knots.

Provides a new perspective on the relationship between Thurston norm and knot surgeries.

Abstract

Two Dehn surgeries on a knot are called cosmetic if they yield homeomorphic manifolds. For a null-homologous knot with certain conditions on the Thurston norm of the ambient manifold, if the knot admits cosmetic surgeries, then the surgery coefficients are equal up to sign.