Conformal Automorphism Groups, Adapted Generating Sets and Bases
Abstract
Let S be a compact Riemann surfaces of genus g >= 2 and G a conformal automoprhism group of order n acting on S. In this paper we give the definition of an adapted generating set and an adapted basis for the first homology group of such a compact Riemann surface. This generating set and basis reflect the action of G in as simple manner as possible. This can be seen in the matrix of the action of G which we obtain. We prove the existence of such a generating set and basis for any conformal group acting on such a surface and find the matrix. This extends our earlier results on adapted bases and matrices for automorphism groups of prime orders and other specific groups.
Cite
@article{arxiv.1711.07797,
title = {Conformal Automorphism Groups, Adapted Generating Sets and Bases},
author = {Jane Gilman},
journal= {arXiv preprint arXiv:1711.07797},
year = {2017}
}
Comments
This Version has expository changes and improvements and some typos corrected