Colored alexander invariants and cone-manifolds

Jun Murakami

    Research output: Contribution to journal › Article

    12 Citations (Scopus)

    Abstract

    In this paper, we reconstruct the link invariant of framed links introduced in [1] by the universal R-matrix of Uq(sl2) and name it the colored Alexander invariant. We check that the optimistic limit o-lim of this invariant is determined by the volume of the knot and link cone-manifold for figure eight knot, Whitehead link and Borromean rings. We also propose the A-polynomials of these examples obtained from the colored Alexander invariant.

    Original languageEnglish
    Pages (from-to)541-564
    Number of pages24
    JournalOsaka Journal of Mathematics
    Volume45
    Issue number2
    Publication statusPublished - 2008 Jun

    Fingerprint

    Cone
    Knot
    Invariant
    Borromean rings
    Link Invariants
    A-polynomial
    R-matrix
    Figure

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Colored alexander invariants and cone-manifolds. / Murakami, Jun.

    In: Osaka Journal of Mathematics, Vol. 45, No. 2, 06.2008, p. 541-564.

    Research output: Contribution to journal › Article

    Murakami, J 2008, 'Colored alexander invariants and cone-manifolds', Osaka Journal of Mathematics, vol. 45, no. 2, pp. 541-564.
    Murakami J. Colored alexander invariants and cone-manifolds. Osaka Journal of Mathematics. 2008 Jun;45(2):541-564.
    Murakami, Jun. / Colored alexander invariants and cone-manifolds. In: Osaka Journal of Mathematics. 2008 ; Vol. 45, No. 2. pp. 541-564.
    @article{7a4c358f217646598483728ba817b9ee,
    title = "Colored alexander invariants and cone-manifolds",
    abstract = "In this paper, we reconstruct the link invariant of framed links introduced in [1] by the universal R-matrix of Uq(sl2) and name it the colored Alexander invariant. We check that the optimistic limit o-lim of this invariant is determined by the volume of the knot and link cone-manifold for figure eight knot, Whitehead link and Borromean rings. We also propose the A-polynomials of these examples obtained from the colored Alexander invariant.",
    author = "Jun Murakami",
    year = "2008",
    month = "6",
    language = "English",
    volume = "45",
    pages = "541--564",
    journal = "Osaka Journal of Mathematics",
    issn = "0030-6126",
    publisher = "Osaka University",
    number = "2",

    }

    TY - JOUR

    T1 - Colored alexander invariants and cone-manifolds

    AU - Murakami, Jun

    PY - 2008/6

    Y1 - 2008/6

    N2 - In this paper, we reconstruct the link invariant of framed links introduced in [1] by the universal R-matrix of Uq(sl2) and name it the colored Alexander invariant. We check that the optimistic limit o-lim of this invariant is determined by the volume of the knot and link cone-manifold for figure eight knot, Whitehead link and Borromean rings. We also propose the A-polynomials of these examples obtained from the colored Alexander invariant.

    AB - In this paper, we reconstruct the link invariant of framed links introduced in [1] by the universal R-matrix of Uq(sl2) and name it the colored Alexander invariant. We check that the optimistic limit o-lim of this invariant is determined by the volume of the knot and link cone-manifold for figure eight knot, Whitehead link and Borromean rings. We also propose the A-polynomials of these examples obtained from the colored Alexander invariant.

    UR - http://www.scopus.com/inward/record.url?scp=47749126179&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=47749126179&partnerID=8YFLogxK

    M3 - Article

    VL - 45

    SP - 541

    EP - 564

    JO - Osaka Journal of Mathematics

    JF - Osaka Journal of Mathematics

    SN - 0030-6126

    IS - 2

    ER -

    Access to Document