Reidemeister transformations of the potential function and the solution

Jinseok Cho, Jun Murakami

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    The potential function of the optimistic limit of the colored Jones polynomial and the construction of the solution of the hyperbolicity equations were defined in the authors' previous papers. In this paper, we define the Reidemeister transformations of the potential function and the solution by the changes of them under the Reidemeister moves of the link diagram and show the explicit formulas. These two formulas enable us to see the changes of the complex volume formula under the Reidemeister moves. As an application, we can simply specify the discrete faithful representation of the link group by showing a link diagram and one geometric solution.

    Original languageEnglish
    Article number1750079
    JournalJournal of Knot Theory and its Ramifications
    Volume26
    Issue number12
    DOIs
    Publication statusPublished - 2017 Oct 1

    Keywords

    • boundary-parabolic representation
    • hyperbolic volume
    • link group
    • optimistic limit
    • Reidemeister moves

    ASJC Scopus subject areas

    • Algebra and Number Theory

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