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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 (n+1)–component Brunnian links can be expressed as a quadratic form on the Milnor μ̄ 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 (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