Abstract
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.
Citation
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
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