Knot Floer homology, genus bounds, and mutation

Details Knot Floer homology, genus bounds, and mutation Knot Floer homology, genus bounds, and mutation

2003-03-18

arxiv.org/abs/math/0303225v2

Mathematics

Geometric Topology

minor revisions, updated references

Scientific paper

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 ($n\leq 9$). Our calculations prove that many of the knots considered here admit no Seifert fibered surgeries.

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