Milnor link invariants and quantum 3-manifold invariants

Let Z(M) be the 3-manifold invariant of Le, Murakami and Ohtsuki. We show t hat Z(M) = 1 + o(n), where o(n) denotes terms of degree greater than or equ al to n, if M is a homology 3-sphere obtained from S-3 by surgery on an n-c omponent Brunnian link whose Milnor <(mu)over bar>-invariants of length les s than or equal to 2n vanish. We prove a realization theorem which is a partial converse to the above the orem. Using the Milnor filtration on links, we define a new bifiltration on the Q vector space with basis the set of oriented diffeomorphism classes of homo logy 3-spheres. This includes the Milnor level 2 filtration defined by Ohts uki. We show that the Milnor level 2 and level 3 filtrations coincide after reindexing.