Group Actions on cyclic covers of the projective line

Kontogeorgis, Aristides and Paramantzoglou, Panagiotis

Abstract

We use tools from combinatorial group theory in order to study actions of three types on groups acting on a curve, namely the automorphism group of a compact Riemann surface, the mapping class group acting on a surface (which now is allowed to have some points removed) and the absolute Galois group \(\mathrm{Gal}( \bar{\mathbb{Q}} /\mathbb{Q})\) in the case of cyclic covers of the projective line.