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The geometry of the Gauss-Picard modular group

Falbel, Elisha; Francsics, Gabor; Parker, John R


Elisha Falbel

Gabor Francsics


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.


Falbel, E., Francsics, G., & Parker, J. R. (2011). The geometry of the Gauss-Picard modular group. Mathematische Annalen, 349(2), 459-508.

Journal Article Type Article
Publication Date Feb 1, 2011
Deposit Date May 26, 2011
Journal Mathematische Annalen
Print ISSN 0025-5831
Electronic ISSN 1432-1807
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 349
Issue 2
Pages 459-508
Publisher URL