Existence of a nonarithmetic lattice in SU(2,1).
The proof of the well-known conjecture that lattices in groups of R-rank greater than 1 are arithmetic has raised speculation about the existence of nonarithmetic lattices in the R-rank 1 group SU(n,1), n > 1. This paper presents an example of such a lattice Gamma(1). Gamma(1) consists of the intersection with SU(2,1) of a group Gamma generated by three complex reflections of order 5. The quotient SU(2,1)/Gamma(1) is compact.
Mostow
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Department of Mathematics, Yale University, New Haven, Connecticut 06520.