A note on knot Floer homology of links

Ni, Yi

doi:10.2140/gt.2006.10.695

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A note on knot Floer homology of links

Yi Ni

Geometry & Topology 10 (2006) 695–713

DOI: 10.2140/gt.2006.10.695

arXiv: math.GT/0506208

Abstract

Ozsváth and Szabó proved that knot Floer homology determines the genera of knots in $S^{3}$ . We will generalize this deep result to links in homology 3–spheres, by adapting their method. Our proof relies on a result of Gabai and some constructions related to foliations. We also interpret a theorem of Kauffman in the world of knot Floer homology, hence we can compute the top filtration term of the knot Floer homology for alternative links.

Keywords

knot Floer homology, links, homology 3–sphere, maximal Euler characteristic, taut foliations, alternative links

Mathematical Subject Classification 2000

Primary: 57R58, 53D40

Secondary: 57M27, 57R30

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Publication

Received: 11 June 2005

Revised: 6 January 2006

Accepted: 9 May 2006

Published: 21 June 2006

Proposed: Peter Ozsváth

Seconded: Rob Kirby, Jim Bryan

Authors

Yi Ni
Department of Mathematics Princeton University Princeton, NJ 08544 USA

Volume 10, issue 2 (2006)