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Knot Floer homology and Seifert surfaces

Andras Juhasz

math.GTarXiv:math/0702514

Abstract

Let K be a knot in S3 of genus g and let n>0. We show that if rk HFK(K,g) < 2n+1 (where HFK denotes knot Floer homology), in particular if K is an alternating knot such that the leading coefficient ag of its Alexander polynomial satisfies |ag| <2n+1, then K has at most n pairwise disjoint non-isotopic genus g Seifert surfaces. For n=1 this implies that K has a unique minimal genus Seifert surface up to isotopy.

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