2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66827In an earlier paper, we introduced a collection of graded Abelian groups $\HFKa(Y,K)$ associated to knots in a three-manifold. The aim of the present paper is to investigate these groups for several specific families of knots, including the Kinoshita-Terasaka knots and their ``Conway mutants''. These results show that $\HFKa$ contains more information than the Alexander polynomial and the signature of these knots; and they also illustrate the fact that $\HFKa$ detects mutation. We also calculate $\HFKa$ for certain pretzel knots, and knots with small crossing number ($n\leq 9$). Our calculations prove that many of the knots considered here admit no Seifert fibered surgeries.minor revisions, updated referencesGeometric TopologySymplectic Geometry57R58, 57M, 53D40text