Hyperbolic manifolds according to Thurston and Jørgensen

  title={Hyperbolic manifolds according to Thurston and J{\o}rgensen},
  author={M. Gromov},
© Association des collaborateurs de Nicolas Bourbaki, 1979-1980, tous droits reserves. L’acces aux archives du seminaire Bourbaki (http://www.bourbaki. ens.fr/) implique l’accord avec les conditions generales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systematique est constitutive d’une infraction penale. Toute copie ou impression de ce fichier doit contenir la presente mention de copyright. 
Volume and bounded cohomology
© Publications mathématiques de l’I.H.É.S., 1982, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » ( http://www.Expand
Non-arithmetic groups in lobachevsky spaces
© Publications mathématiques de l’I.H.É.S., 1987, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http://Expand
Counting commensurability classes of hyperbolic manifolds
Gromov and Piatetski-Shapiro proved existence of finite volume non-arithmetic hyperbolic manifolds of any given dimension. In dimension four and higher, we show that there are about vv such manifoldsExpand
Thick/Thin Decomposition of Three-Manifolds and the Geometrisation Conjecture
These notes are intended to be an introduction to the geometrisation of 3-manifold. The goal is not to give detailed proofs of the results presented here, but mainly to emphasize geometric propertiesExpand
Oeljeklaus–Toma manifolds and arithmetic invariants
We consider Oeljeklaus–Toma manifolds coming from number fields with precisely one complex place. Our general theme is to relate the geometry to the arithmetic. We show that just knowing theExpand
Factorial growth rates for the number of hyperbolic 3-manifolds of a given volume
The work of J{\o}rgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. In this paper, we construct examples showing that theExpand
On the structure of hyperbolic manifolds
Forn≥2, we quantify the Margulis constant ε(n) giving rise to a thick and thin decomposition of hyperbolicn-manifolds of finite volume. As a consequence, we obtain new universal lower bounds for theExpand
Laplacian on Riemannian manifolds
Preamble : This are informal notes of a series of 4 talks I gave in Carthage, as introduction to the Dido Conference, May 24-May 29, 2010. The goal is to present different aspects of the classicalExpand
Kleinian Groups and Hyperbolic Manifolds
As indicated in the Preface, this book is written for those with a reasonable knowledge of Kleinian groups and hyperbolic 3-manifolds, with the aim of extending their repertoire in this area toExpand
Mostow's Rigidity Theorem
Mostow’s Rigidity Theorem is a stunning bridge between the worlds of geometry and topology. It tells us that the geometry of closed hyperbolic n-manifolds, for n ≥ 3, is completely determined byExpand


Simplices of maximal volume in hyperbolicn-space
An n-simplex in H n with vertices v0, ..., v , 6 Hn U ~H ~ is the dosed subset of Hn bounded by the n + I spheres which contain all the vertices except one and which are orthogonal to S "-1. kExpand
Strong Rigidity of Locally Symmetric Spaces.
*Frontmatter, pg. i*Contents, pg. v* 1. Introduction, pg. 1* 2. Algebraic Preliminaries, pg. 10* 3. The Geometry of chi : Preliminaries, pg. 20* 4. A Metric Definition of the Maximal Boundary, pg.Expand