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# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

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

### Tom 214 / 2011

Fundamenta Mathematicae 214 (2011), 161-180 MSC: Primary 30F10; Secondary 30F40, 30F50. DOI: 10.4064/fm214-2-4

#### Streszczenie

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.

#### Autorzy

• Rubén A. HidalgoDepartamento de Matemática
Universidad Técnica Federico Santa María
Casilla 110-V
Valparaíso, Chile
e-mail

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