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Mathematische Annalen

, Volume 349, Issue 2, pp 459–508 | Cite as

The geometry of the Gauss–Picard modular group

  • Elisha FalbelEmail author
  • Gábor Francsics
  • John R. Parker
Article

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.

Mathematics Subject Classification (2000)

51M10 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Elisha Falbel
    • 1
    Email author
  • Gábor Francsics
    • 2
  • John R. Parker
    • 3
  1. 1.Institut de MathématiquesUniversité Pierre et Marie CurieParisFrance
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA
  3. 3.Department of Mathematical SciencesDurham UniversityDurhamUK

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