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

Tu Quoc Thang Le, Jun Murakami

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

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
Volume168
Issue number3
DOIs
Publication statusPublished - 1995 Apr
Externally publishedYes

Fingerprint

Iterated integral
Tangles
Isotopy
Invariant
End point
Extremes
configurations
Generalise
Configuration

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

Representation of the category of tangles by Kontsevich's iterated integral. / Le, Tu Quoc Thang; Murakami, Jun.

In: Communications in Mathematical Physics, Vol. 168, No. 3, 04.1995, p. 535-562.

Research output: Contribution to journalArticle

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