Every compact Nil 3-manifold occurs as a cusp cross-section either in all arithmetic commensurability classes or in exactly one, and also in some non-arithmetic complex hyperbolic or H^2_C-manifold.
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Nil 3-manifolds and cusps of complex hyperbolic surfaces
Every compact Nil 3-manifold occurs as a cusp cross-section either in all arithmetic commensurability classes or in exactly one, and also in some non-arithmetic complex hyperbolic or H^2_C-manifold.