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arXiv · 1404.4965

Tables of quasi-alternating knots with at most 12 crossings

Slavik Jablan
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Abstract

We are giving tables of quasi-alternating knots with $8\le n \le 12$ crossings. As the obstructions for a knot to be quasialternating we used homology thickness with regards to Khovanov homology, odd homology, and Heegaard-Floer homology $\widehat{HFK}$. Except knots which are homology thick, so cannot be quasialternating, by using the results of our computations [JaSa1], for one of knots which are homology thin, knot $11n_{50}$, J. Greene proved that it is not quasi-alternating, so this is the first example of homologically thin knot which is not quasi-alternating [Gr]. In this paper we provide a few more candidates for homology thin knots for which the method used by J. Greene cannot be used to prove that they are not quasialternating. All computations were performed by A. Shumakovitch's program \emph{KhoHo}, the program \emph{Knotscape}, the package \emph{Knot Atlas} by Dror Bar-Natan, and our program \emph{LinKnot}.

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Slavik Jablan. 2014-04-22. Tables of quasi-alternating knots with at most 12 crossings. https://arxiv.org/abs/1404.4965

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