Acta Mathematica

New constructions of fundamental polyhedra in complex hyperbolic space

Martin Deraux, Elisha Falbel, and Julien Paupert

Full-text: Open access

Article information

Source
Acta Math. Volume 194, Number 2 (2005), 155-201.

Dates
Received: 17 August 2004
First available in Project Euclid: 31 January 2017

Permanent link to this document
http://projecteuclid.org/euclid.acta/1485891729

Digital Object Identifier
doi:10.1007/BF02393220

Zentralblatt MATH identifier
1113.22010

Rights
2005 © Institut Mittag-Leffler

Citation

Deraux, Martin; Falbel, Elisha; Paupert, Julien. New constructions of fundamental polyhedra in complex hyperbolic space. Acta Math. 194 (2005), no. 2, 155--201. doi:10.1007/BF02393220. http://projecteuclid.org/euclid.acta/1485891729.


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References

  • Coxeter, H. S. M., Regular Complex Polytopes, 2nd edition. Cambridge Univ. Press, Cambridge 1991.
  • Deligne, P. & Mostow, G. D., Monodromy of hypergeometric functions and nonlattice integral monodromy. Inst. Hautes Études Sci. Publ. Math., 63 (1986), 5–89.
  • Deraux, M., Dirichlet domains for the Mostow lattices Preprint.
  • Falbel, E. & Koseleff, P.-V., Rigldity and flexibility of triangle groups in complex hyperblic geometry. Topology, 41 (2002), 767–786.
  • Falbel, E. & Parker, J. R., The geometry of the Eisenstein-Picard modular group. To appear in Duke Math. J.
  • Falbel, E. & Paupert, J. Fundamental domains for finite subgroups in U(2) and configurations of Lagrangians. Geom. Dedicata, 109 (2004), 221–238.
  • Giraud, G., Sur certaines fonctions automorphes de deux variables. Ann. Sci École Norm. Sup. (3), 38 (1921), 43–164.
  • Goldman, W. M., Complex Hyperbolic Geometry. Oxford Univ. Press, New York, 1999.
  • Maskit, B., Kleinian Groups. Grundlehren Math. Wiss., 287. Springer, Berlin, 1988.
  • Mostow, G. D., On a remarkable class of polyhedra in complex hyperbolic space. Pacific J. Math., 86 (1980), 171–276.
  • —, Generalized Picard lattices arising from half-integral conditions. Inst. Hautes Études Sci. Publ. Math., 63 (1986), 91–106.
  • Picard, É., Sur les fonctions hyperfuchsiennes provenant des séries hypergéométriques de deux variables. Ann. Sci. École Norm. Sup. (3) 2 (1885), 357–384.
  • Schwartz, R. E., Real hyperbolic on the outside, complex hyperbolic on the inside. Invent. Math., 151 (2003), 221–295.
  • —, Complex hyperbolic triangle groups, in Proceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), pp. 339–349, Higher Ed. Press, Beijing, 2002.