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• W2951743531 abstract "We 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." @default.
• W2951743531 created "2019-06-27" @default.
• W2951743531 creator A5013939711 @default.
• W2951743531 creator A5061984117 @default.
• W2951743531 date "1999-05-12" @default.
• W2951743531 modified "2023-09-28" @default.
• W2951743531 title "The colored Jones polynomials and the simplicial volume of a knot" @default.
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