Conformal Automorphism Groups, Adapted Generating Sets and Bases

Jane Gilman

Published 2017-11-21Version 1

In this paper we give the definition of an adapted generating set and an adapted basis for the first homology group of a compact Riemann surface of genus at least two when the surface has a conformal automorphism group of order $n$. We prove the existence of such a generating set and basis for any conformal group acting on a surface. This extends earlier results on adapted bases for automorphism groups of prime orders and other specific groups.