Orateur
Description
P_1-Anosov representations in O(2,n) arise as holonomies of maximal globally hyperbolic conformally flat spacetimes with compact Cauchy hypersurfaces (abbrev. MGHC) . In this talk, we address the converse question: Is the holonomy of a MGHC conformally flat spacetime P_1-Anosov? We investigate this problem in the setting of spacetimes whose universal cover admits a unique maximal point in its causal boundary. Our main result classifies these spacetimes and provides an answer to the above question. We prove that they are all obtained as quotients of regular domains in Minkowski spacetime by discrete groups of conformal transformations. Moreover, when the conformal factor is non-trivial, we show that the corresponding holonomy representation is P_1-Anosov in O(2,n). This is joint work with Thierry Barbot.
