Let be the 3-manifold invariant of Le, Murakami and Ohtsuki. We show that , where denotes terms of degree , if M is a homology 3-sphere obtained from by surgery on an n-component Brunnian link whose Milnor -invariants of length vanish. We prove a realization theorem which is a partial converse to the above theorem.¶Using the Milnor filtration on links, we define a new bifiltration on the vector space with basis the set of oriented diffeomorphism classes of homology 3-spheres. This includes the Milnor level 2 filtration defined by Ohtsuki. We show that the Milnor level 2 and level 3 filtrations coincide after reindexing.
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N. Habegger, Kent E. Orr, Milnor link invariants and quantum 3-manifold invariants. Comment. Math. Helv. 74 (1999), no. 2, pp. 322–344DOI 10.1007/S000140050092