Knot Floer homology and rational surgeries

Abstract

Let $K$ be a rationally null-homologous knot in a three-manifold $Y$. We construct a version of knot Floer homology in this context, including a description of the Floer homology of a three-manifold obtained as Morse surgery on the knot $K$. As an application, we express the Heegaard Floer homology of rational surgeries on $Y$ along a null-homologous knot $K$ in terms of the filtered homotopy type of the knot invariant for $K$. This has applications to Dehn surgery problems for knots in $S^3$. In a different direction, we use the techniques developed here to calculate the Heegaard Floer homology of an arbitrary Seifert fibered three-manifold.

62 pages, 5 figures

References in corpus (5)

• Knot Floer homology and the four-ball genus
• Holomorphic disks and genus bounds
• On the Ozsvath-Szabo invariant of negative definite plumbed 3-manifolds
• On symplectic fillings
• Cosmetic surgeries on genus one knots

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