A note on knot Floer homology of links

Yi Ni

doi:10.2140/gt.2006.10.695

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Home > Journals > Geom. Topol. > Volume 10 > Issue 2 > Article

2006 A note on knot Floer homology of links

Yi Ni

Geom. Topol. 10(2): 695-713 (2006). DOI: 10.2140/gt.2006.10.695

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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.