Article (Scientific journals)
Variétés lorentziennes plates vues comme limites de variétés anti-de Sitter, d'après Danciger, Guéritaud et Kassel
Schlenker, Jean-Marc
2016In Astérisque, 380, p. 475–497
 

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Abstract :
[en] A survey on the recent work of Danciger, Gu\'eritaud and Kassel on Margulis space-times and complete anti-de Sitter space-times. Margulis space-times are quotients of the 3-dimensional Minkowski space by (non-abelian) free groups acting propertly discontinuously. Goldman, Labourie and Margulis have shown that they are determined by a convex co-compact hyperbolic surface S along with a first-order deformation of the metric which uniformly decreases the lengths of closed geodesics. Danciger, Gu\'eritaud and Kassel show that those space-times are principal ℝ-bundles over S with time-like geodesics as fibers, that they are homeomorphic to the interior of a handlebody, and that they admit a fundamental domain bounded by crooked planes. To obtain those results they show that those Margulis space-times are "infinitesimal" versions of 3-dimensional anti-de Sitter manifolds, and are lead to introduce a new parameterization of the space of deformations of a hyperbolic surface that increase the lengths of all closed geodesics.
Disciplines :
Mathematics
Author, co-author :
Schlenker, Jean-Marc ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Variétés lorentziennes plates vues comme limites de variétés anti-de Sitter, d'après Danciger, Guéritaud et Kassel
Alternative titles :
[fr] Flat Lorentzian manifolds as limits of anti-de Sitter manifolds, following Danciger, Guéritaud and Kassel
Publication date :
2016
Journal title :
Astérisque
ISSN :
0303-1179
Publisher :
Société mathématique de France, France
Volume :
380
Pages :
475–497
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