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- Title
The Milnor degree of a 3-manifold.
- Authors
Cochran, Tim; Melvin, Paul
- Abstract
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).
- Subjects
THREE-manifolds (Topology); MILNOR fibration; INVARIANTS (Mathematics); TORSION products; NILPOTENT groups
- Publication
Journal of Topology, 2010, Vol 3, Issue 2, p405
- ISSN
1753-8416
- Publication type
Article
- DOI
10.1112/jtopol/jtq011