Invariants of handlebody-knots via yokota's invariants

Atsuhiko Mizusawa, Jun Murakami

Research output: Contribution to journalArticle

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 1

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint Dive into the research topics of 'Invariants of handlebody-knots via yokota's invariants'. Together they form a unique fingerprint.

  • Cite this