abstract: We give a geometric description of causal properties of (2+1)-dimensional spacetimes with negative cosmological constant (in short, AdS-spacetimes), with three main applications:
-- properness of causal actions (to be defined) of discrete groups of AdS-isometries on their causal domains (to be defined),
-- classification of globally hyperbolic AdS-spacetimes (in dimension $2+1$) with cauchy-complete cauchy surfaces,
-- proposal of a mathematical definition, and description, of black-holes contained in causal AdS-spacetimes, including the family of BTZ black-holes.
Causal AdS-spacetimes