Computations of Heegaard-Floer knot homology

John A. Baldwin; W. D. Gillam

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Computations of Heegaard-Floer knot homology

John A. Baldwin·W. D. Gillam

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Abstract

Using a combinatorial approach described in a recent paper of Manolescu, Ozsváth, and Sarkar we compute the Heegaard-Floer knot homology of all knots with at most 12 crossings as well as the $τ$ invariant for knots through 11 crossings. We review the basic construction of \cite{MOS}, giving two examples that can be worked out by hand, and explain some ideas we used to simplify the computation. We conclude with a discussion of knot Floer homology for small knots, closely examining the Kinoshita-Teraska knot $KT_{2,1}$ and its Conway mutant.

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John A. Baldwin, W. D. Gillam. 2007-01-29. Computations of Heegaard-Floer knot homology. https://arxiv.org/abs/math/0610167

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