Abstract
In this chapter we take up the Milnor invariants, higher order linking numbers, of a link in the 3-sphere, together with the Fox free differential calculus as a basic tool. By the analogy between a link group and a Galois group with restricted ramification in Chap. 7 , we introduce arithmetic analogues of the Milnor invariants for prime numbers by using the pro-l Fox differential calculus, and show that they may be regarded as multiple generalization of the power residue symbol and the Rédei triple symbol.
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