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We give a new construction of fundamental domains in H 2 C for the action of certain lattices in P U (2, 1) defined by Mostow. The polyhedra are given a natural geometric description starting from certain fixed points of elliptic elements. Among the advantages over Dirichlet domains, we gain a simplification of the combinatorics and obtain proofs using… (More)
We describe an experimental method for studying the combinatorics of Dirichlet domains in the complex hyperbolic plane, based on numerical and graphical techniques. We apply our techniques to the complex reflection groups that appear in Mostow's seminal paper on the subject, and list a number of corrections to the combinatorics of the Dirichlet domains.
We produce a family of new, non-arithmetic lattices in PU(2, 1). All previously known examples were commensurable with lattices constructed by Picard, Mostow, and Deligne– Mostow, and fell into 9 commensurability classes. Our groups produce 5 new distinct commensurability classes. Most of the techniques are completely general, and provide efficient… (More)
We show that the figure eight knot complement admits a unique complete spherical CR structure with unipotent boundary holonomy.
The goal of this paper is to give a conjectural census of complex hyperbolic sporadic triangle groups. We prove that only finitely many of these sporadic groups are lattices. We also give a conjectural list of all lattices among sporadic groups, and for each group in the list we give a conjectural group presentation, as well as a list of cusps and… (More)
We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P 1 , and classify the forgetful maps that extend to a map of orbifolds between the stable completions. The cases where this happens include the Livné fibrations and the Mostow/Toledo maps between complex hyperbolic surfaces. They also include a retrac-tion of a 3-dimensional… (More)