Martin Deraux

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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 give a new construction of fundamental domains in H C for the action of certain lattices in PU(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 mainly(More)
We study forgetful maps between Deligne-Mostow moduli spaces of weighted points on P, 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 retraction of a 3-dimensional(More)
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 consider the discrete representations of 3-manifold groups into PU(2, 1) that appear in the Falbel-Koseleff-Rouillier, such that the peripheral subgroups have cyclic unipotent holonomy. We show that two of these representations have conjugate images, even though they represent different 3-manifold groups. This illustrates the fact that a discrete(More)
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