Geometry & Topology 13 (2009) 2991–3019

DOI: 10.2140/gt.2009.13.2991

Abstract

We prove that, for a link L in a rational homology 3–sphere, the link Floer homology detects the Thurston norm of its complement. This result has been proved by Ozsváth and Szabó for links in S³. As an ingredient of the proof, we show that knot Floer homology detects the genus of null-homologous links in rational homology spheres, which is a generalization of an earlier result of the author. Our argument uses the techniques due to Ozsváth and Szabó, Hedden and the author.

Keywords

link Floer homology, link, rational homology 3-sphere, Thurston norm, taut foliation

Mathematical Subject Classification

Primary: 57M27, 57R58

Secondary: 57R30

References

Publication

Received: 8 May 2006
Revised: 2 July 2009
Accepted: 1 August 2009
Published: 18 September 2009
Proposed: Peter Ozsváth
Seconded: Ron Fintushel, Walter Neumann

Authors