Quantum morphing and the Jones polynomial

Authors

Oliver T. Dasbach, University of California, Riverside
Thang D. Le, University of California, Riverside
Xiao Song Lin, University of California, Riverside

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