From colored Jones invariants to logarithmic invariants

Jun Murakami*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number2
Publication statusPublished - 2018


  • Hyperbolic volume
  • Knot theory
  • Quantum group

ASJC Scopus subject areas

  • Mathematics(all)


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