2003/03/18 by Peter Ozsváth, Peter Ozsvath, Ozsvath, Peter +2 · 1 citation
Computer Science · Mathematics · #53D40 #57M #57R58 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:53D40 #msc:57M #msc:57R58 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0303225
minor revisions, updated references
openalex publication_date 2003/03/18 · arxiv created 2004/03/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 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≤ 9). Our calculations prove that many of the knots considered here admit no Seifert fibered surgeries.