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 S³. 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

Primary: 53D40, 57R58

Secondary: 57M27, 57R30

References

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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