The Milnor degree of a 3‐manifold
The Milnor degree of a 3‐manifold
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3 流形的 Milnor 次
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
P. Melvin
中科院分区：
文献类型：
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作者：
Tim D. Cochran;P. Melvin
The Milnor degree of a 3‐manifold is an invariant that records the maximum simplicity, in terms of higher‐order linking, of any link in the 3‐sphere that can be surgered to give the manifold. This invariant is investigated in the context of torsion linking forms, nilpotent quotients of the fundamental group, Massey products and quantum invariants, and the existence of 3‐manifolds with any prescribed Milnor degree and first Betti number is established. Along the way, it is shown that the number Mrk of linearly independent Milnor invariants of degree k, for r‐component links in the 3‐sphere whose lower degree invariants vanish, is positive except in the classically known cases (when r = 1, and when r = 2 with k = 2, 4 or 6).
