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The geometry of the Gauss-Picard modular group.

Falbel, Elisha and Francsics, Gabor and Parker, John R. (2011) 'The geometry of the Gauss-Picard modular group.', Mathematische annalen., 349 (2). pp. 459-508.


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.

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Date of first online publication:February 2011
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