### 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 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Communications in Mathematical Physics*,

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

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

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 168, no. 3, pp. 535-562. https://doi.org/10.1007/BF02101842

}

TY - JOUR

T1 - Representation of the category of tangles by Kontsevich's iterated integral

AU - Le, Tu Quoc Thang

AU - Murakami, Jun

PY - 1995/4

Y1 - 1995/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21844514961&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844514961&partnerID=8YFLogxK

U2 - 10.1007/BF02101842

DO - 10.1007/BF02101842

M3 - Article

AN - SCOPUS:21844514961

VL - 168

SP - 535

EP - 562

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -