A sufficiently complicated noded Schottky group of rank three

Abstract

The theoretical existence of non-classical Schottky groups is due to Marden. Explicit examples of such kind of groups are only known in rank two, the first one by by Yamamoto in 1991 and later by Williams in 2009. In 2006, Maskit and the author provided a theoretical method to obtain examples of non-classical Schottky groups in any rank. The method assumes the knowledge of some algebraic limits of Schottky groups, called sufficiently complicated noded Schottky groups, whose existence was stated. In this paper we provide an explicit construction of a sufficiently complicated noded Schottky group of rank three and it is explained how to construct explicit non-classical Schottky groups of rank three.