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2013 On sutured Floer homology and the equivalence of Seifert surfaces
Matthew Hedden, András Juhász, Sucharit Sarkar
Algebr. Geom. Topol. 13(1): 505-548 (2013). DOI: 10.2140/agt.2013.13.505

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.

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Matthew Hedden. András Juhász. Sucharit Sarkar. "On sutured Floer homology and the equivalence of Seifert surfaces." Algebr. Geom. Topol. 13 (1) 505 - 548, 2013. https://doi.org/10.2140/agt.2013.13.505

Information

Received: 9 March 2011; Accepted: 7 October 2012; Published: 2013
First available in Project Euclid: 19 December 2017

zbMATH: 1272.57008
MathSciNet: MR3116378
Digital Object Identifier: 10.2140/agt.2013.13.505

Subjects:
Primary: 57M27
Secondary: 57R58

Rights: Copyright © 2013 Mathematical Sciences Publishers

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