Algebraic & Geometric Topology

On sutured Floer homology and the equivalence of Seifert surfaces

Matthew Hedden, András Juhász, and Sucharit Sarkar

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Abstract

The goal of this paper is twofold. First, given a Seifert surface R in the 3–sphere, we show how to construct a Heegaard diagram for the sutured manifold S3(R) complementary to R, which in turn enables us to compute the sutured Floer homology of S3(R) combinatorially. Secondly, we outline how the sutured Floer homology of S3(R), together with the Seifert form of R, can be used to decide whether two minimal genus Seifert surfaces of a given knot are isotopic in S3. We illustrate our techniques by showing that the knot 83 has two minimal genus Seifert surfaces up to isotopy. Furthermore, for any n1 we exhibit a knot Kn that has at least n nonisotopic free minimal genus Seifert surfaces.

Article information

Source
Algebr. Geom. Topol., Volume 13, Number 1 (2013), 505-548.

Dates
Received: 9 March 2011
Accepted: 7 October 2012
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715505

Digital Object Identifier
doi:10.2140/agt.2013.13.505

Mathematical Reviews number (MathSciNet)
MR3116378

Zentralblatt MATH identifier
1272.57008

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

Keywords
Heegaard diagram Seifert surface Floer homology

Citation

Hedden, Matthew; Juhász, András; Sarkar, Sucharit. On sutured Floer homology and the equivalence of Seifert surfaces. Algebr. Geom. Topol. 13 (2013), no. 1, 505--548. doi:10.2140/agt.2013.13.505. https://projecteuclid.org/euclid.agt/1513715505


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