Let be a knot in of genus and let We show that if (where denotes knot Floer homology), in particular if is an alternating knot such that the leading coefficient of its Alexander polynomial satisfies then has at most pairwise disjoint nonisotopic genus Seifert surfaces. For this implies that has a unique minimal genus Seifert surface up to isotopy.
"Knot Floer homology and Seifert surfaces." Algebr. Geom. Topol. 8 (1) 603 - 608, 2008. https://doi.org/10.2140/agt.2008.8.603