Algebraic & Geometric Topology

Knot Floer homology and rational surgeries

Peter S Ozsváth and Zoltán Szabó

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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.

Article information

Algebr. Geom. Topol., Volume 11, Number 1 (2011), 1-68.

Received: 22 May 2005
Revised: 14 September 2010
Accepted: 17 September 2010
First available in Project Euclid: 19 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R58: Floer homology
Secondary: 57M27: Invariants of knots and 3-manifolds 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Floer homology Dehn surgery


Ozsváth, Peter S; Szabó, Zoltán. Knot Floer homology and rational surgeries. Algebr. Geom. Topol. 11 (2011), no. 1, 1--68. doi:10.2140/agt.2011.11.1.

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