Milnor's link invariants attached to certain Galois groups over $\mathbf {Q}$

Abstract

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 a tip of an arithmetical theory after the model of link theory which may give a new insight in algebraic number theory. The details will be published elsewhere.