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Stoimenow, Alexander

Rational knots and a theorem of Kanenobu. (English) Zbl 0964.57004

Exp. Math. 9, No. 3, 473-478 (2000).
In the paper [Math. Ann. 285, No. 1, 115-124 (1989; Zbl 0651.57006)], T. Kanenobu showed that for a rational or \(2\)-bridge knot or link, the Jones polynomial \(V\) and the Brandt-Lickorish-Millett-Ho polynomial \(Q\) satisfy \((-u-u^{-1})(Q(-u-u^{-1})-1) = 2(V(u)V(u^{-1}) -1).\) This relation provides a criterion to decide the nonrationality of a knot.
In the paper under review the author gives some series of examples where Kanenobu’s necessary condition for the rationality is not sufficient.
Reviewer: Sang Youl Lee (Pusan)

Cited in 2 Documents

MSC:

57M25 Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

rational knot; Jones polynomial; \(Q\)-polynomial

Citations:

Zbl 0651.57006; Zbl 0668.57012
PDFBibTeX XMLCite
\textit{A. Stoimenow}, Exp. Math. 9, No. 3, 473--478 (2000; Zbl 0964.57004)
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References:

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