### 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 language | English |
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Pages (from-to) | 535-562 |

Number of pages | 28 |

Journal | Communications in Mathematical Physics |

Volume | 168 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1995 Apr 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Le, T. Q. T., & Murakami, J. (1995). Representation of the category of tangles by Kontsevich's iterated integral.

*Communications in Mathematical Physics*,*168*(3), 535-562. https://doi.org/10.1007/BF02101842