2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228077The 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.This is the version published by Algebraic & Geometric Topology on 25 September 2006Geometric Topology57M25, 57M27text