Knot Floer homology and rational surgeries

2005/04/20 by Peter Ozsvath, Zoltan Szabo · 1 citation
Mathematics · #math.GT #math.SG

paper · pdf · doi:10.2140/agt.2011.11.1

published as Algebr. Geom. Topol. 11 (2011) 1-68 · 62 pages, 5 figures

arxiv created 2005/04/20 · arxiv updated 2014/09/30

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 S³. In a different direction, we use the techniques developed here to calculate the Heegaard Floer homology of an arbitrary Seifert fibered three-manifold.

Cited by

• The next-to-top term of the knot Floer homology of some non-fibered knots