Computations of Heegaard-Floer knot homology

Details Computations of Heegaard-Floer knot homology Computations of Heegaard-Floer knot homology

2006-10-05

arxiv.org/abs/math/0610167v3

Mathematics

Geometric Topology

28 pages, 5 figures. We added a computation of the \tau invariant for knots through 11 crossings as well as a computation of \

Scientific paper

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 $\tau$ 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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