The colored Jones polynomials and the simplicial volume of a knot

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dc.creatorMurakami, Hitoshi
dc.creatorMurakami, Jun
dc.date1999-05-12
dc.date1999-06-10
dc.date.accessioned2026-07-07T05:29:03Z
dc.date.available2026-07-07T05:29:03Z
dc.descriptionWe show that the set of colored Jones polynomials and the set of generalized Alexander polynomials defined by Akutsu, Deguchi and Ohtsuki intersect non-trivially. Moreover it is shown that the intersection is (at least includes) the set of Kashaev's quantum dilogarithm invariants for links. Therefore Kashaev's conjecture can be restated as follows: The colored Jones polynomials determine the hyperbolic volume for a hyperbolic knot. Modifying this, we propose a stronger conjecture: The colored Jones polynomials determine the simplicial volume for any knot. If our conjecture is true, then we can prove that a knot is trivial if and only if all of its Vassiliev invariants are trivial.
dc.description18 pages. Added Remark 2.2 and improved Remark 5.7
dc.identifierhttps://arxiv.org/abs/math/9905075
dc.identifierhttp://arxiv.org/abs/math/9905075
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78493
dc.subjectGeometric Topology
dc.subjectQuantum Algebra
dc.subject57M25; 57M50; 17B37; 81R50
dc.titleThe colored Jones polynomials and the simplicial volume of a knot
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