Abstract
This chapter presents the examples of the non-arithmetic lattices in hyperbolic spaces of arbitrary dimension. In these examples the lattices are generated by reflections. Vinberg gave a general theory of groups that was generated by reflections in Lobachevsky spaces. Using this theory he gave examples of non-arithmetic lattices for dimensions four and five. The existence of non-arithmetic lattices for other symmetric spaces of rank one is known for spaces of Hermitian type of dimension two or three. These examples were obtained by Mostow using his theory of quasireflections.
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Schedule a callMore From: Number Theory, Trace Formulas and Discrete Groups: Symposium in Honor of Atle Selberg Oslo, Norway, July 14—21, 1987
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