Singular sets and parameters of generalized triangle orbifolds

Details Singular sets and parameters of generalized triangle orbifolds Singular sets and parameters of generalized triangle orbifolds

2001-03-03

arxiv.org/abs/math/0103015v3

Mathematics

Metric Geometry

19 pages, many figures

Scientific paper

We study groups generated by three half-turns in Lobachevsky space and their factor-orbifolds. This generalized triangle groups are directly connected with the arbitrary 2-generator Kleinian groups. Our main result is a complete description of the singular sets of the generalized triangle orbifolds. We also give a method to obtain the parameters defining a generalized triangle group from the structure of the singular set of its factor-orbifold and illustrate it by examples.

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