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Milnor’s link invariants attached to certain Galois groups over \(\mathbb Q\). (English) Zbl 0990.11068

Summary: This is a résumé of the author’s recent work on certain analogies between primes and links. The purpose of this article is to introduce a new invariant, called Milnor invariant, in algebraic number theory, based on an analogy between the structure of a certain Galois group over the rational number field and that of the group of a link in three-dimensional Euclidean space. It then turns out that the Legendre, Rédei symbols are interpreted as our link invariants. We expect that this is the tip of an arithmetical theory related to the model of link theory which may give a new insight in algebraic number theory. The details will be published elsewhere.

MSC:

11R32 Galois theory
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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