Computations of Heegaard-Floer knot homology
Abstract
Using a combinatorial approach described in a recent paper of Manolescu, Ozsv\'ath, 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 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 KT2,1 and its Conway mutant.
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