On the Kontsevich integral of Brunnian links

Habiro, Kazuo¹ ; Meilhan, Jean-Baptiste¹

¹Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan

Algebraic and Geometric Topology, Tome 6 (2006) no. 3, pp. 1399-1412

Résumé

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.

Détail

DOI : 10.2140/agt.2006.6.1399

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

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