Knot Floer homology and rational surgeries

Ozsváth, Peter S; Szabó, Zoltán

doi:10.2140/agt.2011.11.1

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Knot Floer homology and rational surgeries

Peter S Ozsváth and Zoltán Szabó

Algebraic & Geometric Topology 11 (2011) 1–68

DOI: 10.2140/agt.2011.11.1

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 with even first Betti number.

Keywords

Floer homology, Dehn surgery

Mathematical Subject Classification 2000

Primary: 57R58

Secondary: 57M27, 57M25

References

Publication

Received: 22 May 2005

Revised: 14 September 2010

Accepted: 17 September 2010

Published: 6 January 2010

Authors

Peter S Ozsváth
Department of Mathematics Columbia University New York, NY 10027 USA
http://www.math.columbia.edu/~petero/
Zoltán Szabó
Department of Mathematics Princeton University Princeton, NJ 08540 USA
http://www.math.princeton.edu/~szabo/

Volume 11, issue 1 (2011)