## Algebraic & Geometric Topology

### Knot Floer homology and Seifert surfaces

Andras Juhasz

#### 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
Revised: 25 February 2008
Accepted: 25 February 2008
First available in Project Euclid: 20 December 2017

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

#### 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