The geometry of the Gauss-Picard modular group.

Abstract

We give a construction of a fundamental domain for PU(2,1,\mathbbZ [i])PU(21Z[i]), that is the group of holomorphic isometries of complex hyperbolic space with coefficients in the Gaussian ring of integers \mathbbZ [i]Z[i]. We obtain from that construction a presentation of that lattice and relate it, in particular, to lattices constructed by Mostow.