From colored Jones invariants to logarithmic invariants

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper, we express the logarithmic invariant of knots in terms of derivatives of the colored Jones invariants. Logarithmic invariant is defined by using the Jacobson radicals of the restricted quantum group Ūξ (sl2) where ξ is a root of unity. We also propose a version of the volume conjecture stating a relation between the logarithmic invariants and the hyperbolic volumes of the cone manifolds along a knot, which is proved for the figure-eight knot.

Original languageEnglish
Pages (from-to)453-475
Number of pages23
JournalTokyo Journal of Mathematics
Volume41
Issue number2
DOIs
Publication statusPublished - 2018 Jan 1

Fingerprint

Logarithmic
Knot
Invariant
Hyperbolic Volume
Jacobson Radical
Roots of Unity
Quantum Groups
Figure
Cone
Express
Derivative

Keywords

  • Hyperbolic volume
  • Knot theory
  • Quantum group

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

From colored Jones invariants to logarithmic invariants. / Murakami, Jun.

In: Tokyo Journal of Mathematics, Vol. 41, No. 2, 01.01.2018, p. 453-475.

Research output: Contribution to journalArticle

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