Title
Quantum morphing and the Jones polynomial
Document Type
Article
Publication Date
12-1-2001
Abstract
We will explore the experimental observation that on the set of knots with bounded crossing number, algebraically independent Vassiliev invariants become correlated, as noticed first by S. Willerton. We will see this through the value distribution of the Jones polynomial at roots of unit. As the degree of the roots of unit is getting larger, the higher order fluctuation is diminishing and a more organized shape will emerge from a rather random value distribution of the Jones polynomial. We call such a phenomenon "quantum morphing". Evaluations of the Jones polynomial at roots of unity play a crucial role, for example in the volume conjecture.
Publication Source (Journal or Book title)
Communications in Mathematical Physics
First Page
427
Last Page
442
Recommended Citation
Dasbach, O., Le, T., & Lin, X. (2001). Quantum morphing and the Jones polynomial. Communications in Mathematical Physics, 224 (2), 427-442. https://doi.org/10.1007/s002200100543