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arXiv · math/0303225

Knot Floer homology, genus bounds, and mutation

Peter Ozsvath·Zolta Szabo
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Abstract

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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Peter Ozsvath, Zolta Szabo. 2004-03-02. Knot Floer homology, genus bounds, and mutation. https://arxiv.org/abs/math/0303225

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