Actions on Symmetric curves from the Arithmetic Topology viewpoint

Kontogeorgis, Aristides and Paramantzoglou, Panagiotis

Abstract

We give an explanation of the MKR dictionary in Arithmetic topology using Ihara's theory of profinite braid groups. Motivated by the analogy we perform explicit computations for representations of both braid groups and the absolute Galois group \(\mathrm\{Gal\}(\bar\{\Q\}/\Q)\) for cyclic covers of the projective line and generalized Fermat curves.