Volume 11, issue 1 (2011)

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Knot Floer homology and rational surgeries

Peter S Ozsváth and Zoltán Szabó

Algebraic & Geometric Topology 11 (2011) 1–68

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 S3. In a different direction, we use the techniques developed here to calculate the Heegaard Floer homology of an arbitrary Seifert fibered three-manifold with even first Betti number.

Floer homology, Dehn surgery
Mathematical Subject Classification 2000
Primary: 57R58
Secondary: 57M27, 57M25
Received: 22 May 2005
Revised: 14 September 2010
Accepted: 17 September 2010
Published: 6 January 2010
Peter S Ozsváth
Department of Mathematics
Columbia University
New York, NY 10027
Zoltán Szabó
Department of Mathematics
Princeton University
Princeton, NJ 08540