Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 11, Number 1 (2011), 1-68.
Knot Floer homology and rational surgeries
Let be a rationally null-homologous knot in a three-manifold . 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 . As an application, we express the Heegaard Floer homology of rational surgeries on along a null-homologous knot in terms of the filtered homotopy type of the knot invariant for . This has applications to Dehn surgery problems for knots in . 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.
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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. https://projecteuclid.org/euclid.agt/1513715180