Link Floer homology detects the Thurston norm

Ni, Yi

doi:10.2140/gt.2009.13.2991

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Link Floer homology detects the Thurston norm

Yi Ni

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 $S^{3}$ . 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 2000

Primary: 57R58, 57M27

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

Yi Ni
Department of Mathematics Columbia University MC 4406 2990 Broadway New York, NY 10027

Volume 13, issue 5 (2009)