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.
"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