Abstract
We study proper, isometric actions of nonsolvable discrete groups Γ on the 3-dimensional Minkowski space R as limits of actions on the 3-dimensional anti-de Sitter space AdS. To each such action is associated a deformation of a hyperbolic surface group Γ0 inside O(2, 1). When Γ0 is convex cocompact, we prove that Γ acts properly on R if and only if this group-level deformation is realized by a deformation of the quotient surface that everywhere contracts distances at a uniform rate. We give two applications in this case. (1) Tameness: A complete flat spacetime is homeomorphic to the interior of a compact manifold. (2) Geometric transition: A complete flat spacetime is the rescaled limit of collapsing AdS spacetimes.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Annales scientifiques de l'École normale supérieure
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
