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