#### Volume 6, issue 3 (2006)

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On the Kontsevich integral of Brunnian links

### Kazuo Habiro and Jean-Baptiste Meilhan

Algebraic & Geometric Topology 6 (2006) 1399–1412
 arXiv: math.GT/0605312
##### Abstract

The purpose of the paper is twofold. First, we give a short proof using the Kontsevich integral for the fact that the restriction of an invariant of degree $2n$ to $\left(n+1\right)$–component Brunnian links can be expressed as a quadratic form on the Milnor $\stackrel{̄}{\mu }$ link-homotopy invariants of length $n+1$. Second, we describe the structure of the Brunnian part of the degree–$2n$ graded quotient of the Goussarov–Vassiliev filtration for $\left(n+1\right)$–component links.

##### Mathematical Subject Classification 2000
Primary: 57M25, 57M27
##### Publication
Revised: 3 July 2006
Accepted: 7 July 2006
Published: 25 September 2006
##### Authors
 Kazuo Habiro Research Institute for Mathematical Sciences Kyoto University Kyoto 606-8502 Japan Jean-Baptiste Meilhan Research Institute for Mathematical Sciences Kyoto University Kyoto 606-8502 Japan