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 Γ₁. Γ₁ consists of the intersection with SU(2,1) of a group Γ generated by three complex reflections of order 5. The quotient SU(2,1)/Γ₁ is compact.