A rationality conjecture about Kontsevich integral of knots and its implications to the structure of the colored Jones polynomial

dc.creatorRozansky, L.
dc.date2001-06-12
dc.date.accessioned2026-07-07T04:42:07Z
dc.date.available2026-07-07T04:42:07Z
dc.descriptionWe 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.descriptionLaTeX, 35 pages, 3 pictures
dc.identifierhttps://arxiv.org/abs/math/0106097
dc.identifierhttp://arxiv.org/abs/math/0106097
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61640
dc.subjectGeometric Topology
dc.subjectQuantum Algebra
dc.subject57M27
dc.titleA rationality conjecture about Kontsevich integral of knots and its implications to the structure of the colored Jones polynomial
dc.typetext

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