Abstract.
Let \( {\cal Z}(M) \) be the 3-manifold invariant of Le, Murakami and Ohtsuki. We show that \( {\cal Z}(M) = 1 + o(n) \), where \( o(n) \) denotes terms of degree \( \geq n \), if M is a homology 3-sphere obtained from \( S^3 \) by surgery on an n-component Brunnian link whose Milnor \( \overline\mu \)-invariants of length \( \leq 2n \) 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 \( \Bbb Q \) 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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Received: October 23, 1998.
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Habegger, N., Orr, K. Milnor link invariants and quantum 3-manifold invariants. Comment. Math. Helv. 74, 322–344 (1999). https://doi.org/10.1007/s000140050092
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DOI: https://doi.org/10.1007/s000140050092