Singular sets and parameters of generalized triangle orbifolds

Abstract

We study groups generated by three half-turns in the Lobachevsky $3$-space and their quotient orbifolds. These generalized triangle groups are closely related to the arbitrary 2-generator Kleinian groups. Our main result is a classification of the singular sets of the generalized triangle orbifolds. We also present a method to obtain the parameters defining a generalized triangle group from the structure of the singular set of its quotient orbifold and illustrate it by examples.

v4: 20 pages, many figures; the mathematical part is unchanged from 2002, the text is revised to improve readability

References in corpus (1)

• On arithmetic Kleinian groups generated by three half-turns