Computations of Heegaard-Floer knot homology
Abstract
Description
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.
28 pages, 5 figures. We added a computation of the τinvariant for knots through 11 crossings as well as a computation of \hat{HFK} for all non-alternating 12 crossing knots
28 pages, 5 figures. We added a computation of the τinvariant for knots through 11 crossings as well as a computation of \hat{HFK} for all non-alternating 12 crossing knots