Link Floer homology detects the Thurston norm

Ni, Yi¹

¹ Department of Mathematics, Columbia University, MC 4406, 2990 Broadway, New York, NY 10027

Geometry & topology, Tome 13 (2009) no. 5, pp. 2991-3019.

Résumé

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.

Détail

DOI : 10.2140/gt.2009.13.2991

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

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