On the Kontsevich integral of Brunnian links

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 $\bar{\mu }$ 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.