TY - JOUR
T1 - New non-arithmetic complex hyperbolic lattices
AU - Deraux, Martin
AU - Parker, John R.
AU - Paupert, Julien
N1 - Funding Information:
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.
Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - We produce a family of new, non-arithmetic lattices in (Formula presented.). 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.
AB - We produce a family of new, non-arithmetic lattices in (Formula presented.). 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.
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U2 - 10.1007/s00222-015-0600-1
DO - 10.1007/s00222-015-0600-1
M3 - Article
AN - SCOPUS:84958877864
VL - 203
SP - 681
EP - 771
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
SN - 0020-9910
IS - 3
ER -