Knot Floer homology and Seifert surfaces

Abstract

Let K be a knot in S^3 of genus g and let n>0. We show that if rk HFK(K,g) < 2^{n+1} (where HFK denotes knot Floer homology), in particular if K is an alternating knot such that the leading coefficient a_g of its Alexander polynomial satisfies |a_g| <2^{n+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.

4 pages, n=0 case corrected

References in corpus (3)

• Knot Floer homology detects fibred knots
• Floer homology and surface decompositions
• Holomorphic discs and sutured manifolds

Cited by in corpus (2)

• Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial
• Floer homology and non-fibered knot detection