FINITE TYPE INVARIANTS AND MILNOR INVARIANTS FOR BRUNNIAN LINKS

Abstract

A link L in the 3-sphere is called Brunnian if every proper sublink of L is trivial. In a previous paper, Habiro proved that the restriction to Brunnian links of any Goussarov–Vassiliev finite type invariant of (n + 1)-component links of degree < 2n is trivial. The purpose of this paper is to study the first nontrivial case. We show 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 link-homotopy invariants of length n + 1.