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Dehn surgery and nonseparating two-spheres

### Jennifer Hom and Tye Lidman

Vol. 5 (2022), No. 1, 145–153
##### Abstract

When can surgery on a nullhomologous knot $K$ in a rational homology sphere produce a nonseparating 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.

##### Keywords
Dehn surgery, Heegaard Floer homology
##### Mathematical Subject Classification
Primary: 57K10, 57K18, 57K30