Invariants of handlebody-knots via yokota's invariants

Atsuhiko Mizusawa, Jun Murakami

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    2 Citations (Scopus)

    Abstract

    We construct quantum $\mathcal{U}-q(\mathfrak{sl}-{2})$ type invariants for handlebody-knots in the 3-sphere S3. A handlebody-knot is an embedding of a handlebody in a 3-manifold. These invariants are linear sums of Yokota's invariants for colored spatial graphs which are defined by using the Kauffman bracket. We give a table of calculations of our invariants for genus 2 handlebody-knots up to six crossings. We also show our invariants are identified with special cases of the Witten-Reshetikhin-Turaev invariants.

    Original languageEnglish
    Article number1350068
    JournalJournal of Knot Theory and its Ramifications
    Volume22
    Issue number11
    DOIs
    Publication statusPublished - 2013 Oct

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    Keywords

    • Handlebody-knot
    • quantum invariant
    • WRT invariants
    • Yokota's invariants

    ASJC Scopus subject areas

    • Algebra and Number Theory

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