Geodesic
Knot Floer homology and rational surgeries
Ozsváth, Peter S1 ; Szabó, Zoltán2
1Department of Mathematics, Columbia University, New York, NY 10027, USA
2Department of Mathematics, Princeton University, Princeton, NJ 08540, USA
Algebraic and Geometric Topology, Tome 11 (2011) no. 1, pp. 1-68
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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.

DOI : 10.2140/agt.2011.11.1
Keywords: Floer homology, Dehn surgery

Ozsváth, Peter S  1   ; Szabó, Zoltán  2

1 Department of Mathematics, Columbia University, New York, NY 10027, USA
2 Department of Mathematics, Princeton University, Princeton, NJ 08540, USA 
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Ozsváth, Peter S; Szabó, Zoltán. Knot Floer homology and rational surgeries. Algebraic and Geometric Topology, Tome 11 (2011) no. 1, pp. 1-68. doi: 10.2140/agt.2011.11.1

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