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We consider symmetric complex hyperbolic triangle groups generated by three complex reeec-tions with angle 2=p. We restrict our attention to those groups where certain words are elliptic. Our goal is to nd necessary conditions for such a group to be discrete. The main application we have in mind is that such groups are candidates for non-arithmetic lattices(More)
The purpose of this paper is twofold. First, we give a survey of the known methods of constructing lattices in complex hyperbolic space. Secondly, we discuss some of the lattices constructed by Deligne and Mostow and by Thurston in detail. In particular, we give a unified treatment of the constructions of fundamental domains and we relate this to other(More)
We give a version of Shimizu's lemma for groups of complex hyperbolic isometries one of whose generators is a parabolic screw motion. Suppose that G is a discrete group containing a parabolic screw motion A and let B be any element of G not fixing the fixed point of A. Our result gives a bound on the radius of the isometric spheres of B and B −1 in terms of(More)