Algebraic & Geometric Topology

Knot Floer homology and Seifert surfaces

Andras Juhasz

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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.

Article information

Source
Algebr. Geom. Topol., Volume 8, Number 1 (2008), 603-608.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796824

Digital Object Identifier
doi:10.2140/agt.2008.8.603

Mathematical Reviews number (MathSciNet)
MR2443240

Zentralblatt MATH identifier
1144.57007

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds 57R58: Floer homology

Keywords
Alexander polynomial Seifert surface Floer homology

Citation

Juhasz, Andras. Knot Floer homology and Seifert surfaces. Algebr. Geom. Topol. 8 (2008), no. 1, 603--608. doi:10.2140/agt.2008.8.603. https://projecteuclid.org/euclid.agt/1513796824


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