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On sutured Floer
homology and the equivalence of Seifert surfaces
Matthew Hedden, András Juhász and Sucharit Sarkar |
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Algebraic & Geometric Topology 13 (2013) 505–548
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Abstract |
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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. |
Keywords
Heegaard diagram, Seifert surface, Floer homology
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57R58
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References |
Publication
Received: 9 March 2011
Accepted: 7 October 2012
Published: 10 March 2013
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Authors |
| Matthew Hedden | |
| Department of Mathematics Michigan State University East Lansing, MI 48824 USA |
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| http://www.math.msu.edu/~mhedden/Site/Home.html | |
| András Juhász | |
| Department of Mathematics South Kensington Campus, Imperial College London SW7 2AZ UK |
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| http://www2.imperial.ac.uk/~ajuhasz/ | |
| Sucharit Sarkar | |
| Department of Mathematics Princeton University Princeton, NJ 08544 USA |
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