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Cubo (Temuco)

On-line version ISSN 0719-0646

Cubo vol.22 no.1 Temuco Apr. 2020

http://dx.doi.org/10.4067/S0719-06462020000100039 

Articles

A sufficiently complicated noded Schottky group of rank three

Rubén A. Hidalgo1 

1 Departamento de Matemática y Estadística, Universidad de La Frontera, Temuco, Chile. ruben.hidalgo@ufrontera.cl

Abstract

In 1974, Marden proved the existence of non-classical Schottky groups by a theoretical and non-constructive argument. Explicit examples are only known in rank two; the first one by Yamamoto in 1991 and later by Williams in 2009. In 2006, Maskit and the author provided a theoretical method to construct non-classical Schottky groups in any rank. The method assumes the knowledge of certain algebraic limits of Schottky groups, called sufficiently complicated noded Schottky groups. The aim of this paper is to provide explicitly a sufficiently complicated noded Schottky group of rank three and explain how to use it to construct explicit non-classical Schottky groups.

Resumen

En 1974, Marden demostró la existencia de grupos de Schottky no-clásicos con un argumento teórico y no-constructivo. Se conocen ejemplos explícitos solo en rango dos; el primero por Yamamoto en 1991 y después por Williams en 2009. En 2006, Maskit y el autor entregaron un método teórico para construir grupos de Schottky no-clásicos en cualquier rango. El método asume el conocimiento de ciertos límites algebraicos de grupos de Schottky, llamados grupos de Schottky anodados suficientemente complicados. El objetivo de este paper es dar un grupo de Schottky anodado suficientemente complicado explícitamente de rango tres y explicar cómo usarlo para construir grupos de Schottky no-clásicos explícitos.

Keywords and Phrases: Riemann surfaces; Schottky groups

Texto completo disponible sólo en PDF.

Full text available only in PDF format.

Acknowledgement.

Partially supported by Projects Fondecyt 1190001.

References

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