On the Kontsevich integral of Brunnian links

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 mu-bar 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.