On the Kontsevich integral of Brunnian links

Habiro, Kazuo; Meilhan, Jean-Baptiste

doi:10.2140/agt.2006.6.1399

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On the Kontsevich integral of Brunnian links

Kazuo Habiro and Jean-Baptiste Meilhan

Algebraic & Geometric Topology 6 (2006) 1399–1412

DOI: 10.2140/agt.2006.6.1399

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 $2 n$ to $(n + 1)$ –component Brunnian links can be expressed as a quadratic form on the Milnor $\bar{μ}$ link-homotopy invariants of length $n + 1$ . Second, we describe the structure of the Brunnian part of the degree– $2 n$ graded quotient of the Goussarov–Vassiliev filtration for $(n + 1)$ –component links.

Keywords

Brunnian links, Goussarov–Vassiliev invariants, Milnor link-homotopy invariants, Kontsevich integral

Mathematical Subject Classification 2000

Primary: 57M25, 57M27

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Publication

Received: 10 January 2006

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

Volume 6, issue 3 (2006)