Arithmetic Topology in Ihara Theory

Abstract

Ihara initiated the study of a certain Galois representation that may be seen as an arithmetic analogue of the Artin representation of a pure braid group. We pursue the analogies in Ihara theory further and give foundational results, following some issues and their interrelations in the theory of braids and links such as Milnor invariants, Johnson homomorphisms, Magnus–Gassner cocycles and Alexander invariants, and study relations with arithmetic in Ihara theory.