Inventiones mathematicae

, Volume 203, Issue 3, pp 681–771 | Cite as

New non-arithmetic complex hyperbolic lattices

  • Martin Deraux
  • John R. Parker
  • Julien PaupertEmail author


We produce a family of new, non-arithmetic lattices in \({\mathrm{PU}}(2,1)\). All previously known examples were commensurable with lattices constructed by Picard, Mostow, and Deligne–Mostow, and fell into nine commensurability classes. Our groups produce five new distinct commensurability classes. Most of the techniques are completely general, and provide efficient geometric and computational tools for constructing fundamental domains for discrete groups acting on the complex hyperbolic plane.



The authors would like to thank the following institutions for their support during the preparation of this paper, in chronological order: the University of Utah, Université de Fribourg, Durham University, Université de Grenoble, Arizona State University. The authors acknowledge support from the ANR through the program “Structures Géométriques et Triangulations”, NSF Grants DMS 1107452, 1107263, 1107367 (the GEAR Network) and ICERM at Brown University. The third author was also partially supported by SNF Grant 200020-121506/1 and NSF Grant DMS 1007340/1249147. The authors would also like to thank Bernard Parisse and Fabrice Rouillier for useful assistance on the computational aspects, as well as the referee for several suggestions which improved the exposition of the paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Martin Deraux
    • 1
  • John R. Parker
    • 2
  • Julien Paupert
    • 3
    Email author
  1. 1.Institut FourierUniversité de Grenoble 1Saint-Martin d’ HèresFrance
  2. 2.Department of Mathematical SciencesDurham UniversityDurhamUK
  3. 3.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA

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