Vol. 257, No. 1, 2012

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Arithmeticity of complex hyperbolic triangle groups

Matthew Stover

Vol. 257 (2012), No. 1, 243–256

Complex hyperbolic triangle groups, originally studied by Mostow in building the first nonarithmetic lattices in PU(2,1), are a natural generalization of the classical triangle groups. A theorem of Takeuchi states that there are only finitely many Fuchsian triangle groups that determine an arithmetic lattice in PSL2(), so triangle groups are generically nonarithmetic. We prove similar finiteness theorems for complex hyperbolic triangle groups that determine an arithmetic lattice in PU(2,1).

complex hyperbolic geometry, arithmetic lattices, complex hyperbolic triangle groups
Mathematical Subject Classification 2010
Primary: 11F06, 20H10, 22E40
Received: 12 October 2011
Revised: 30 November 2011
Accepted: 5 December 2011
Published: 19 June 2012
Matthew Stover
Department of Mathematics
University of Michigan
530 Church Street
Ann Arbor, MI 48109
United States