Advertisement

Acta Mathematica

, Volume 194, Issue 2, pp 155–201 | Cite as

New constructions of fundamental polyhedra in complex hyperbolic space

  • Martin Deraux
  • Elisha Falbel
  • Julien Paupert
Article

Keywords

Hyperbolic Space Complex Hyperbolic Space Fundamental Polyhedron 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [C]
    Coxeter, H. S. M.,Regular Complex Polytopes, 2nd edition. Cambridge Univ. Press, Cambridge 1991.zbMATHGoogle Scholar
  2. [DM]
    Deligne, P. &Mostow, G. D., Monodromy of hypergeometric functions and nonlattice integral monodromy.Inst. Hautes Études Sci. Publ. Math., 63 (1986), 5–89.MathSciNetzbMATHGoogle Scholar
  3. [De]
    Deraux, M., Dirichlet domains for the Mostow lattices Preprint.Google Scholar
  4. [FK]
    Falbel, E. &Koseleff, P.-V., Rigldity and flexibility of triangle groups in complex hyperblic geometry.Topology, 41 (2002), 767–786.CrossRefMathSciNetzbMATHGoogle Scholar
  5. [FPk]
    Falbel, E. & Parker, J. R., The geometry of the Eisenstein-Picard modular group. To appear inDuke Math. J.Google Scholar
  6. [FPp]
    Falbel, E. &Paupert, J. Fundamental domains for finite subgroups inU(2) and configurations of Lagrangians.Geom. Dedicata, 109 (2004), 221–238.CrossRefMathSciNetzbMATHGoogle Scholar
  7. [Gi]
    Giraud, G., Sur certaines fonctions automorphes de deux variables.Ann. Sci École Norm. Sup. (3), 38 (1921), 43–164.zbMATHMathSciNetGoogle Scholar
  8. [Go]
    Goldman, W. M.,Complex Hyperbolic Geometry. Oxford Univ. Press, New York, 1999.zbMATHGoogle Scholar
  9. [Ma]
    Maskit, B.,Kleinian Groups. Grundlehren Math. Wiss., 287. Springer, Berlin, 1988.zbMATHGoogle Scholar
  10. [Mol]
    Mostow, G. D., On a remarkable class of polyhedra in complex hyperbolic space.Pacific J. Math., 86 (1980), 171–276.zbMATHMathSciNetGoogle Scholar
  11. [Mo2]
    —, Generalized Picard lattices arising from half-integral conditions.Inst. Hautes Études Sci. Publ. Math., 63 (1986), 91–106.zbMATHMathSciNetCrossRefGoogle Scholar
  12. [P]
    Picard, É., Sur les fonctions hyperfuchsiennes provenant des séries hypergéométriques de deux variables.Ann. Sci. École Norm. Sup. (3) 2 (1885), 357–384.zbMATHMathSciNetGoogle Scholar
  13. [S1]
    Schwartz, R. E., Real hyperbolic on the outside, complex hyperbolic on the inside. Invent. Math., 151 (2003), 221–295.zbMATHMathSciNetCrossRefGoogle Scholar
  14. [S2]
    —, Complex hyperbolic triangle groups, inProceedings of the International Congress of Mathematicians, Vol. II (Beijing, 2002), pp. 339–349, Higher Ed. Press, Beijing, 2002.Google Scholar

Copyright information

© Institut Mittag-Leffler 2005

Authors and Affiliations

  • Martin Deraux
    • 1
  • Elisha Falbel
    • 2
  • Julien Paupert
    • 3
  1. 1.Centre de MathématiquesÉcole PolytechniquePalaiseau CedexFrance
  2. 2.Institut de MathématiquesUniversité Pierre et Marie CurieParisFrance
  3. 3.Institut de MathématiquesUniversité Pierre et Marie CurieParisFrance

Personalised recommendations