Volume 10, issue 2 (2006)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A note on knot Floer homology of links

Yi Ni

Geometry & Topology 10 (2006) 695–713

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 2000
Primary: 57R58, 53D40
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
Yi Ni
Department of Mathematics
Princeton University
Princeton, NJ 08544
USA