Collisions of Particles in Locally AdS Spacetimes II Moduli of Globally Hyperbolic Spaces.
Résumé
We investigate globally hyperbolic 3-dimensional AdS manifolds containing " particles " , i.e., cone singularities of angles less than 2π along a time-like graph. To each such space (equipped with a time-like vector field satisfying some additional properties) we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds.