Theory of coverings in the study of Riemann surfaces

Ewa Tyszkowska. "Theory of coverings in the study of Riemann surfaces." Colloquium Mathematicae 127.2 (2012): 173-184. <http://eudml.org/doc/283438>.

@article{EwaTyszkowska2012,
abstract = {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.},
author = {Ewa Tyszkowska},
journal = {Colloquium Mathematicae},
keywords = {Riemann surfaces; automorphism groups; Fuchsian groups},
language = {eng},
number = {2},
pages = {173-184},
title = {Theory of coverings in the study of Riemann surfaces},
url = {http://eudml.org/doc/283438},
volume = {127},
year = {2012},
}

TY - JOUR
AU - Ewa Tyszkowska
TI - Theory of coverings in the study of Riemann surfaces
JO - Colloquium Mathematicae
PY - 2012
VL - 127
IS - 2
SP - 173
EP - 184
AB - 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.
LA - eng
KW - Riemann surfaces; automorphism groups; Fuchsian groups
UR - http://eudml.org/doc/283438
ER -