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Massey products in the cohomology of groups with applications to link theory


Author: David Stein
Journal: Trans. Amer. Math. Soc. 318 (1990), 301-325
MSC: Primary 57M25; Secondary 55S30
DOI: https://doi.org/10.1090/S0002-9947-1990-0958903-3
MathSciNet review: 958903
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Abstract: Invariants of links in $ {S^3}$ are developed using a modification of the Massey product of one-dimensional classes in the cohomology of certain groups. The theory yields two types of invariants, invariants which depend upon a collection of meridians, or basing, of a link, and invariants which do not. The invariants, which are independent of the basing, are compared with John Milnor's $ \overline \mu $-invariants. For two component links, a collection of ostensibly based invariants is shown to be independent of the basing. If the linking number of the components of such a link is zero, the resulting invariants may be equivalent to the Sato-Levine-Cochran invariants.


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DOI: https://doi.org/10.1090/S0002-9947-1990-0958903-3
Article copyright: © Copyright 1990 American Mathematical Society

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