Volume 8, issue 1 (2008)

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Knot Floer homology and Seifert surfaces

Andras Juhasz

Algebraic & Geometric Topology 8 (2008) 603–608
Abstract

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.

Keywords
Alexander polynomial, Seifert surface, Floer homology
Mathematical Subject Classification 2000
Primary: 57M27, 57R58
References
Publication
Received: 7 December 2007
Revised: 25 February 2008
Accepted: 25 February 2008
Published: 12 May 2008
Authors
Andras Juhasz
Department of Mathematics
Princeton University
Princeton, NJ 08544
USA