A rationality conjecture about Kontsevich integral of knots and its implications to the structure of the colored Jones polynomial
| dc.creator | Rozansky, L. | |
| dc.date | 2001-06-12 | |
| dc.date.accessioned | 2026-07-07T04:42:07Z | |
| dc.date.available | 2026-07-07T04:42:07Z | |
| dc.description | We formulate a conjecture (already proven by A. Kricker) about the structure of Kontsevich integral of a knot. We describe its value in terms of the generating functions for the numbers of external edges attached to closed 3-valent diagrams. We conjecture that these functions are rational functions of the exponentials of their arguments, their denominators being the powers of the Alexander-Conway polynomial. This conjecture implies the existence of an expansion of a colored Jones (HOMFLY) polynomial in powers of q-1 whose coefficients are rational functions of q^color. We show how to derive the first Kontsevich integral polynomial associated to the theta-graph from the rational expansion of the colored SU(3) Jones polynomial. | |
| dc.description | LaTeX, 35 pages, 3 pictures | |
| dc.identifier | https://arxiv.org/abs/math/0106097 | |
| dc.identifier | http://arxiv.org/abs/math/0106097 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61640 | |
| dc.subject | Geometric Topology | |
| dc.subject | Quantum Algebra | |
| dc.subject | 57M27 | |
| dc.title | A rationality conjecture about Kontsevich integral of knots and its implications to the structure of the colored Jones polynomial | |
| dc.type | text |