Parallel version of the universal Vassiliev-Kontsevich invariant

Thang T Q Le, Jun Murakami

Research output: Contribution to journalArticle

31 Citations (Scopus)

Abstract

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
Volume121
Issue number3
Publication statusPublished - 1997 Oct 10
Externally publishedYes

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Vassiliev Invariants
Knot
Chord Diagrams
Wilson Loop
Universal Enveloping Algebra
Normalization
Explicit Formula
Lie Algebra
Trivial
Calculate
Invariant
Generalization

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Parallel version of the universal Vassiliev-Kontsevich invariant. / Le, Thang T Q; Murakami, Jun.

In: Journal of Pure and Applied Algebra, Vol. 121, No. 3, 10.10.1997, p. 271-291.

Research output: Contribution to journalArticle

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