Dehn surgery and non-separating two-spheres

TL;DR

This paper investigates conditions under which Dehn surgery on a null-homologous knot in a rational homology sphere yields a non-separating sphere, using Heegaard Floer homology to identify when the knot is unknotted.

Contribution

It provides new sufficient conditions for a knot to be unknotted based on Heegaard Floer homology, with applications to homology cobordism, concordance, and Mazur manifolds.

Findings

Heegaard Floer homology gives criteria for unknottedness after surgery.

Conditions for non-separating spheres in surgered manifolds.

Applications to homology cobordism and Mazur manifolds.

Abstract

When can surgery on a null-homologous knot K in a rational homology sphere produce a non-separating sphere? We use Heegaard Floer homology to give sufficient conditions for K to be unknotted. We also discuss some applications to homology cobordism, concordance, and Mazur manifolds.