The geometry of the Gauss-Picard modular group

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

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.

Citation

Falbel, E., Francsics, G., & Parker, J. R. (2011). The geometry of the Gauss-Picard modular group. Mathematische Annalen, 349(2), 459-508. https://doi.org/10.1007/s00208-010-0515-5

• 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
• DOI: https://doi.org/10.1007/s00208-010-0515-5
• Public URL: https://durham-repository.worktribe.com/output/1531805
• Publisher URL: http://www.springerlink.com/content/45795585237222h8/