The complex volumes of twist knots via colored jones polynomials

Jinseok Cho, Jun Murakami

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    For a hyperbolic knot, an ideal triangulation of the knot complement corresponding to the colored Jones polynomial was introduced by Thurston. Considering this triangulation of a twist knot, we find a function which gives the hyperbolicity equations and the complex volume of the knot complement, using Zickert's theory of the extended Bloch group and the complex volume. We also consider a formal approximation of the colored Jones polynomial. Following Ohnuki's theory of 2-bridge knots, we define another function which comes from the approximation. We show that this function is essentially the same as the previous function, and therefore it also gives the same hyperbolicity equations and the complex volume. Finally we compare this result with our previous one which dealt with Yokota theory, and, as an application to Yokota theory, present a refined formula of the complex volumes for any twist knots.

    Original languageEnglish
    Pages (from-to)1401-1421
    Number of pages21
    JournalJournal of Knot Theory and its Ramifications
    Volume19
    Issue number11
    DOIs
    Publication statusPublished - 2010 Nov

    Fingerprint

    Colored Jones Polynomial
    Twist
    Knot
    Hyperbolicity
    Triangulation
    Complement
    2-bridge Knot
    Hyperbolic Knot
    Approximation

    Keywords

    • colored Jones polynomial
    • complex volume
    • twist knot
    • Volume conjecture

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    The complex volumes of twist knots via colored jones polynomials. / Cho, Jinseok; Murakami, Jun.

    In: Journal of Knot Theory and its Ramifications, Vol. 19, No. 11, 11.2010, p. 1401-1421.

    Research output: Contribution to journalArticle

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