Translator Disclaimer
2011 Knot Floer homology and rational surgeries
Peter S Ozsváth, Zoltán Szabó
Algebr. Geom. Topol. 11(1): 1-68 (2011). DOI: 10.2140/agt.2011.11.1


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.


Download Citation

Peter S Ozsváth. Zoltán Szabó. "Knot Floer homology and rational surgeries." Algebr. Geom. Topol. 11 (1) 1 - 68, 2011.


Received: 22 May 2005; Revised: 14 September 2010; Accepted: 17 September 2010; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1226.57044
MathSciNet: MR2764036
Digital Object Identifier: 10.2140/agt.2011.11.1

Primary: 57R58
Secondary: 57M25, 57M27

Rights: Copyright © 2011 Mathematical Sciences Publishers


Vol.11 • No. 1 • 2011
Back to Top