For a G-covering Y → Y/G = X induced by a properly discontinuous action of a group G on a topological space Y, there is a natural action of π(X,x) on the set F of points in Y with nontrivial stabilizers in G. We study the covering of X obtained from the universal covering of X and the left action of π(X,x) on F. We find a formula for the number of fixed points of an element g ∈ G which is a generalization of Macbeath's formula applied to an automorphism of a Riemann surface. We give a new method for determining subgroups of a given Fuchsian group.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm127-2-3,
author = {Ewa Tyszkowska},
title = {Theory of coverings in the study of Riemann surfaces},
journal = {Colloquium Mathematicae},
volume = {126},
year = {2012},
pages = {173-184},
zbl = {1250.30036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm127-2-3}
}
Ewa Tyszkowska. Theory of coverings in the study of Riemann surfaces. Colloquium Mathematicae, Tome 126 (2012) pp. 173-184. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm127-2-3/