Non-arithmetic groups in Lobachevsky spaces

Michael Gromov; I. Piatetski-Shapiro

Publications Mathématiques de l'IHÉS (1987)

  • Volume: 66, page 93-103
  • ISSN: 0073-8301

How to cite

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Gromov, Michael, and Piatetski-Shapiro, I.. "Non-arithmetic groups in Lobachevsky spaces." Publications Mathématiques de l'IHÉS 66 (1987): 93-103. <http://eudml.org/doc/104029>.

@article{Gromov1987,
author = {Gromov, Michael, Piatetski-Shapiro, I.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {non-arithmetic lattices; projective orthogonal group; arithmetic subgroups; hyperbolic manifolds; universal covering; fundamental group; commensurability},
language = {eng},
pages = {93-103},
publisher = {Institut des Hautes Études Scientifiques},
title = {Non-arithmetic groups in Lobachevsky spaces},
url = {http://eudml.org/doc/104029},
volume = {66},
year = {1987},
}

TY - JOUR
AU - Gromov, Michael
AU - Piatetski-Shapiro, I.
TI - Non-arithmetic groups in Lobachevsky spaces
JO - Publications Mathématiques de l'IHÉS
PY - 1987
PB - Institut des Hautes Études Scientifiques
VL - 66
SP - 93
EP - 103
LA - eng
KW - non-arithmetic lattices; projective orthogonal group; arithmetic subgroups; hyperbolic manifolds; universal covering; fundamental group; commensurability
UR - http://eudml.org/doc/104029
ER -

References

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  1. [B]1 A. BOREL, Introduction aux groupes arithmétiques, Paris, Hermann (1969). Zbl0186.33202MR39 #5577
  2. [B]2 A. BOREL, Linear algebraic groups, New York, Benjamin (1969). Zbl0186.33201MR40 #4273
  3. [G]1 M. GROMOV, Hyperbolic manifolds according to Thurston and Jorgensen, Lecture Notes in Mathematics, 842, Springer-Verlag (1981), pp. 40-54. Zbl0452.51017MR84b:53046
  4. [G]2 M. GROMOV, Rigid transformation groups. To appear. Zbl0652.53023
  5. [M] V. S. MAKAROV, On a certain class of discrete Lobachevsky space groups with infinite fundamental domain of finite measure, Dokl. Ak. Nauk. U.S.S.R., 167 (1966), pp. 30-33. Zbl0146.16502MR34 #244
  6. [Mo] G. MOSTOW, Discrete subgroups of Lie groups, in Elie Cartan et les Mathématiques d'aujourd'hui, Astérisque, numéro hors série (1985), 289-309. Zbl0605.22008MR87j:22017
  7. [N] V. V. NIKULIN, Discrete reflection groups in Lobachevsky space and algebraic surfaces, Preprint. Zbl0671.22006
  8. [R] M. S. RAGHUNATHAN, Discrete subgroups of Lie groups, Springer (1972). Zbl0254.22005MR58 #22394a
  9. [V] E. B. VINBERG, Hyperbolic reflection groups, Usp. Math. Nauk., 40 (1985), pp. 29-66. Zbl0579.51015MR86m:53059
  10. [Z] R. ZIMMER, Ergodic theory and semisimple groups, Birkhauser, Boston (1984). Zbl0571.58015MR86j:22014

Citations in EuDML Documents

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  1. Nicolas Bergeron, Sur l'homologie et le spectre des variétés hyperboliques
  2. Slavyana Geninska, On arithmetic Fuchsian groups and their characterizations
  3. Jean Raimbault, Géométrie et topologie des variétés hyperboliques de grand volume
  4. Michael Gromov, Richard Schoen, Harmonic maps into singular spaces and p -adic superrigidity for lattices in groups of rank one
  5. Daniel Allcock, James A. Carlson, Domingo Toledo, Hyperbolic geometry and moduli of real cubic surfaces
  6. Dietrich Burde, Crystallographic actions on Lie groups and post-Lie algebra structures
  7. Pierre Pansu, Sous-groupes discrets des groupes de Lie : rigidité, arithméticité

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