On Lorentz spacetimes of constant curvature

Abstract

We describe in parallel the Lorentzian homogeneous spaces $G=\mathrm{PSL}(2,\mathbb{R})$ and $\mathfrak{g}=\mathfrak{psl}(2,\mathbb{R})$, and review some recent results relating the geometry of their quotients by discrete groups.

16 pages, 2 figures. Appeared in the Proceedings of the December 2012 conference "Groups, Geometry, Dynamics" (Almora, India). Editors: C.S. Aravinda, W.M. Goldman, K. Gongopadhyay, A. Lubotzky, Mahan Mj, A. Weaver