Knot Floer homology and rational surgeries

DOI10.2140/AGT.2011.11.1zbMATH Open1226.57044arXivmath/0504404OpenAlexW3101555884MaRDI QIDQ618732

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Publication date: 17 January 2011

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/math/0504404

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