On fixed points of automorphisms of non-orientable unbordered Klein surfaces

• Autores: Grzegorz Gromadzki
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 53, Nº 1, 2009, págs. 73-82
• Idioma: inglés
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• Resumen

  • 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 ! 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.