#### Volume 10, issue 2 (2006)

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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 ${S}^{3}$. 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