Parallel version of the universal Vassiliev-Kontsevich invariant

Thang T.Q. Le*, Jun Murakami

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


Let Ẑf be the universal Vassiliev-Kontsevich invariant for framed links in [13], which is a generalization of Kontsevich's invariant in [10, 1]. Let K be a framed knot and K(r) be its r-parallel. Then we show Ẑf(K(r)) = Δ(r)(Ẑf(K)), where Δ(r) is an operation of chord diagrams which replace the Wilson loop by r copies. We calculate the values of Ẑf of the Hopf links and the change of Ẑf under the Kirby moves. An explicit formula of an important normalization factor, which is the value of the trivial knot, in the universal enveloping algebra U(g) of any Lie algebra is given.

Original languageEnglish
Pages (from-to)271-291
Number of pages21
JournalJournal of Pure and Applied Algebra
Issue number3
Publication statusPublished - 1997 Oct 10
Externally publishedYes

ASJC Scopus subject areas

  • Algebra and Number Theory


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