Predicting the number and type of twist sites in a rational knot or link

Mark E. Kidwell; Kerry M. Luse

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arXiv · 1410.0308

Predicting the number and type of twist sites in a rational knot or link

Mark E. Kidwell·Kerry M. Luse

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Abstract

A rational knot or link can be put into a standard alternating format which has horizontal and vertical twist sites (double helices). The number and type of these twist sites are determined by terms of next-to-highest $z$-degree in Kauffman's regular isotopy invariant $Λ(a,z)$. In particular, for a knot or link with $c$ crossings, the coefficient of the $z^{c-2}$ term is equal to the number of twist sites in its standard diagram. Furthermore, the coefficients of the $a^{-2}z^{c-2}$ and $a^2z^{c-2}$ terms count the number of left-turning and right-turning twist sites, respectively.

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BibTeX RIS

Mark E. Kidwell, Kerry M. Luse. 2014-10-01. Predicting the number and type of twist sites in a rational knot or link. https://arxiv.org/abs/1410.0308

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