Representation of the category of tangles by Kontsevich's iterated integral

Tu Quoc Thang Le*, Jun Murakami

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


Applying Kontsevich's iterated integral for tangles, we get an isotopy invariant of tangles. We give a method to compute the integral of a tangle combinatorially from modified integrals of some simple tangles. We localize the integral by moving the end points of the tangle to an extreme configuration, and modify the integral so that it is convergent. By using a similar technique, we generalize Kontsevich's invariant to a framed tangle.

Original languageEnglish
Pages (from-to)535-562
Number of pages28
JournalCommunications in Mathematical Physics
Issue number3
Publication statusPublished - 1995 Apr
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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