Open Access
2009 On fixed points of automorphisms of non-orientable unbordered Klein surfaces
G. Gromadzk
Publ. Mat. 53(1): 73-82 (2009).


In 1973, Macbeath found a general formula for the number of points fixed by an arbitrary orientation preserving automorphism of a Riemann surface $X$. It was given in terms of a group $G$ of conformal automorphisms of $X$ and the ramification data of the covering $X\to X/G$, which corresponds to the so called universal covering transformation group. In these terms, for the case of a cyclic group of automorphisms of an unbordered non-orientable Klein surface, the formula was given later by Izquierdo and Singerman and here we find formulas valid for an arbitrary (finite) group $G$ of automorphisms.


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G. Gromadzk. "On fixed points of automorphisms of non-orientable unbordered Klein surfaces." Publ. Mat. 53 (1) 73 - 82, 2009.


Published: 2009
First available in Project Euclid: 17 December 2008

MathSciNet: MR2474115

Primary: 30F;
Secondary: 14H

Keywords: Automorphisms of Riemann and Klein surfaces , fixed-point set , Fuchsian and NEC-groups , uniformization

Rights: Copyright © 2009 Universitat Autònoma de Barcelona, Departament de Matemàtiques

Vol.53 • No. 1 • 2009
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