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2008 Knot Floer homology and Seifert surfaces
Andras Juhasz
Algebr. Geom. Topol. 8(1): 603-608 (2008). DOI: 10.2140/agt.2008.8.603

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.

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Andras Juhasz. "Knot Floer homology and Seifert surfaces." Algebr. Geom. Topol. 8 (1) 603 - 608, 2008. https://doi.org/10.2140/agt.2008.8.603

Information

Received: 7 December 2007; Revised: 25 February 2008; Accepted: 25 February 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1144.57007
MathSciNet: MR2443240
Digital Object Identifier: 10.2140/agt.2008.8.603

Subjects:
Primary: 57M27, 57R58

Rights: Copyright © 2008 Mathematical Sciences Publishers

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