On the Colored Jones Polynomial and the Kashaev invariant

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dc.creatorHuynh, Vu
dc.creatorLe, Thang T. Q.
dc.date2005-03-15
dc.date.accessioned2026-07-07T05:17:58Z
dc.date.available2026-07-07T05:17:58Z
dc.descriptionWe express the colored Jones polynomial as the inverse of the quantum determinant of a matrix with entries in the $q$-Weyl algebra of $q$-operators, evaluated at the trivial function (plus simple substitutions). The Kashaev invariant is proved to be equal to another special evaluation of the determinant. We also discuss the similarity between our determinant formula of the Kashaev invariant and the determinant formula of the hyperbolic volume of knot complements, hoping it would lead to a proof of the volume conjecture.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math/0503296
dc.identifierhttp://arxiv.org/abs/math/0503296
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74499
dc.subjectGeometric Topology
dc.subjectQuantum Algebra
dc.subject57M25
dc.titleOn the Colored Jones Polynomial and the Kashaev invariant
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