# Theory of coverings in the study of Riemann surfaces

Colloquium Mathematicae (2012)

- Volume: 127, Issue: 2, page 173-184
- ISSN: 0010-1354

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topEwa 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 -

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