In an earlier paper, we introduced a collection of graded Abelian groups HFK(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 HFK contains more information than the Alexander polynomial and the signature of these knots; and they also illustrate the fact that HFK detects mutation. We also calculate HFK for certain pretzel knots, and knots with small crossing number (n≤9). Our calculations give obstructions to certain Seifert fibered surgeries on the knots considered here.
All Science Journal Classification (ASJC) codes
- Geometry and Topology