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Cubo (Temuco)

On-line version ISSN 0719-0646

Abstract

HIDALGO, Rubén A.. A sufficiently complicated noded Schottky group of rank three. Cubo [online]. 2020, vol.22, n.1, pp.39-53. ISSN 0719-0646.  http://dx.doi.org/10.4067/S0719-06462020000100039.

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.

Keywords : Riemann surfaces; Schottky groups.

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