Volume 13, issue 5 (2009)

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Link Floer homology detects the Thurston norm

Yi Ni

Geometry & Topology 13 (2009) 2991–3019
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.

Mathematical Subject Classification 2000
Primary: 57R58, 57M27
Secondary: 57R30
Publication
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