Kashaev's conjecture and the Chern-Simons invariants of knots and links

Hitoshi Murakami, Jun Murakami, Miyuki Okamoto, Toshie Takata, Yoshiyuki Yokota

    Research output: Contribution to journalArticle

    38 Citations (Scopus)

    Abstract

    R. M. Kashaev conjectured that the asymptotic behavior of the link invariant he introduced [Kashaev 95], which equals the colored Jones polynomial evaluated at a root of unity, determines the hyperbolic volume of any hyperbolic link complement. We observe numerically that for knots 63, 89 and 820 and for the Whitehead link, the colored Jones polynomials are related to the hyperbolic volumes and the Chern-Simons invariants and propose a complexification of Kashaev's conjecture.

    Original languageEnglish
    Pages (from-to)427-435
    Number of pages9
    JournalExperimental Mathematics
    Volume11
    Issue number3
    Publication statusPublished - 2002

    Fingerprint

    Hyperbolic Volume
    Colored Jones Polynomial
    Knot
    Link Invariants
    Complexification
    Invariant
    Roots of Unity
    Complement
    Asymptotic Behavior

    Keywords

    • Chern-Simons invariant
    • Colored Jones polynomial
    • Kashaev's conjecture
    • Volume
    • Volume conjecture

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Murakami, H., Murakami, J., Okamoto, M., Takata, T., & Yokota, Y. (2002). Kashaev's conjecture and the Chern-Simons invariants of knots and links. Experimental Mathematics, 11(3), 427-435.

    Kashaev's conjecture and the Chern-Simons invariants of knots and links. / Murakami, Hitoshi; Murakami, Jun; Okamoto, Miyuki; Takata, Toshie; Yokota, Yoshiyuki.

    In: Experimental Mathematics, Vol. 11, No. 3, 2002, p. 427-435.

    Research output: Contribution to journalArticle

    Murakami, H, Murakami, J, Okamoto, M, Takata, T & Yokota, Y 2002, 'Kashaev's conjecture and the Chern-Simons invariants of knots and links', Experimental Mathematics, vol. 11, no. 3, pp. 427-435.
    Murakami, Hitoshi ; Murakami, Jun ; Okamoto, Miyuki ; Takata, Toshie ; Yokota, Yoshiyuki. / Kashaev's conjecture and the Chern-Simons invariants of knots and links. In: Experimental Mathematics. 2002 ; Vol. 11, No. 3. pp. 427-435.
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