Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 13, Number 1 (2013), 505-548.
On sutured Floer homology and the equivalence of Seifert surfaces
The goal of this paper is twofold. First, given a Seifert surface in the –sphere, we show how to construct a Heegaard diagram for the sutured manifold complementary to , which in turn enables us to compute the sutured Floer homology of combinatorially. Secondly, we outline how the sutured Floer homology of , together with the Seifert form of , can be used to decide whether two minimal genus Seifert surfaces of a given knot are isotopic in . We illustrate our techniques by showing that the knot has two minimal genus Seifert surfaces up to isotopy. Furthermore, for any we exhibit a knot that has at least nonisotopic free minimal genus Seifert surfaces.
Algebr. Geom. Topol., Volume 13, Number 1 (2013), 505-548.
Received: 9 March 2011
Accepted: 7 October 2012
First available in Project Euclid: 19 December 2017
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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