Lifting di-analytic involutions of compact Klein surfaces to extended-Schottky uniformizations

Rubén A. Hidalgo¹

¹ Departamento de Matemática Universidad Técnica Federico Santa María Casilla 110-V Valparaíso, Chile

Fundamenta Mathematicae, Tome 214 (2011) no. 2, pp. 161-180.

Résumé

Let $S$ be a compact Klein surface together with a di-analytic involution $\kappa :S \to S$. The lowest uniformizations of $S$ are those whose deck group is an extended-Schottky group, that is, an extended Kleinian group whose orientation preserving half is a Schottky group. If $S$ is a bordered compact Klein surface, then it is well known that $\kappa $ can be lifted with respect to a suitable extended-Schottky uniformization of $S$. In this paper, we complete the above lifting property by proving that if $S$ is a closed Klein surface, then $\kappa $ can also be lifted to a suitable extended-Schottky uniformization.

Détail

DOI : 10.4064/fm214-2-4

Keywords: compact klein surface together di analytic involution kappa lowest uniformizations those whose deck group extended schottky group extended kleinian group whose orientation preserving half schottky group bordered compact klein surface known kappa lifted respect suitable extended schottky uniformization paper complete above lifting property proving closed klein surface kappa lifted suitable extended schottky uniformization