New construction of fundamental domains for certain Mostow groups

Abstract

In this article, we give a new construction of fundamental polyhedra for certain Mostow groups in complex hyperbolic space. The shape of fundamental polyhedra is a natural generalization of the fundamental polyhedron for the sister of Eisenstein-Picard lattice.

New non-arithmetic complex hyperbolic lattices

“…Presentations for various of these groups have been given in several places, including [20], [10], [25], [37] for instance. A unified presentation for all Deligne-Mostow groups with three fold symmetry was given in [28].…”

“…The application of this general strategy in the context of complex hyperbolic space is difficult and subtle, as can be seen in the difficulties in Mostow's proof that were analyzed in [Der05]. It has been successfully carried out in several places, but always for groups closely related to Mostow's (see [DFP05], [Par06], [FP06], [Zha12]). For the groups we consider in this paper, the previously used techniques seem difficult to implement (for instance, the Dirichlet domains we studied in [DPP11] have extremely complicated combinatorial structure).…”

New Nonarithmetic Complex Hyperbolic Lattices II

“…Presentations for various of these groups have been given in several places, including [22], [12], [28], [45] for instance. A unified presentation for all Deligne-Mostow groups with three fold symmetry was given in [32].…”