The Universal R-Matrix, Burau Representaion and the Melvin-Morton Expansion of the Colored Jones Polynomial
| dc.creator | Rozansky, L. | |
| dc.date | 1996-04-03 | |
| dc.date | 1996-05-17 | |
| dc.date.accessioned | 2026-07-07T09:08:38Z | |
| dc.date.available | 2026-07-07T09:08:38Z | |
| dc.description | P. Melvin and H. Morton studied the expansion of the colored Jones polynomial of a knot in powers of q-1 and color. They conjectured an upper bound on the power of color versus the power of q-1. They also conjectured that the bounding line in their expansion generated the inverse Alexander-Conway polynomial. These conjectures were proved by D. Bar-Natan and S. Garoufalidis. We have conjectured that other `lines' in the Melvin-Morton expansion are generated by rational functions with integer coefficients whose denominators are powers of the Alexander-Conway polynomial. Here we prove this conjecture by using the R-matrix formula for the colored Jones polynomial and presenting the universal R-matrix as a `perturbed' Burau matrix. | |
| dc.description | 31 pages, LaTeX (some misprints corrected, references added) | |
| dc.identifier | https://arxiv.org/abs/q-alg/9604005 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9604005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150793 | |
| dc.subject | Quantum Algebra | |
| dc.subject | 57M25 (Primary) 17B37 (Secondary) | |
| dc.title | The Universal R-Matrix, Burau Representaion and the Melvin-Morton Expansion of the Colored Jones Polynomial | |
| dc.type | text |