Vol. 255, No. 2, 2012

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Dirichlet–Ford domains and arithmetic reflection groups

Grant S. Lakeland

Vol. 255 (2012), No. 2, 417–437
Abstract

We show that a Fuchsian group, acting on the upper half-plane model for 2, admits a Ford domain which is also a Dirichlet domain, for some center, if and only if it is an index 2 subgroup of a reflection group. This is used to exhibit an example of a maximal arithmetic hyperbolic reflection group which is not congruence. Analogous results, and counterexamples, are given in the case of Kleinian groups.

Keywords
fundamental domain, arithmetic reflection groups, congruence
Mathematical Subject Classification 2010
Primary: 20H10
Secondary: 19B37
Milestones
Received: 8 March 2011
Accepted: 16 June 2011
Published: 10 April 2012
Authors
Grant S. Lakeland
Department of Mathematics
University of Texas
Austin, TX 78712
United States