Geodesic
Knot Floer homology and Seifert surfaces
Juhasz, Andras1
1Department of Mathematics, Princeton University, Princeton, NJ 08544, USA
Algebraic and Geometric Topology, Tome 8 (2008) no. 1, pp. 603-608
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Let K be a knot in S3 of genus g and let n > 0. We show that if rkHFK̂(K,g) < 2n+1 (where HFK̂ 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 nonisotopic genus g Seifert surfaces. For n = 1 this implies that K has a unique minimal genus Seifert surface up to isotopy.

DOI : 10.2140/agt.2008.8.603
Keywords: Alexander polynomial, Seifert surface, Floer homology

Juhasz, Andras  1

1 Department of Mathematics, Princeton University, Princeton, NJ 08544, USA 
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Juhasz, Andras. Knot Floer homology and Seifert surfaces. Algebraic and Geometric Topology, Tome 8 (2008) no. 1, pp. 603-608. doi: 10.2140/agt.2008.8.603

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