Document Zbl 0991.57012 - zbMATH Open
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Quantum morphing and the Jones polynomial. (English) Zbl 0991.57012
The authors observe that plotting of the suitably-normalized values of Jones polynomial of knots with bounded crossing number at a root of unity in the complex plane shows some correlation. Here the normalization is such that, as the order \(n\) of the root of unity tends to \(\infty\), the real and imaginary parts of the value converge to the first two Vassiliev invariants \(v_2\) and \(v_3\) of the knot. If \(n\) is small, then the plotting looks somewhat random, but, as \(n\) tends larger, the plotting becomes more similar to the more organized plotting of \(v_2\) and \(v_3\) of knots by S. Willerton [On the first two Vassiliev invariants (preprint)]. “Quantum morphing” in the title refers to this phenomenon.
MSC:
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |