2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Collection 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Organisateur(s) Canary, Richard ; Garcia-Faide, Elba ; Labourie, François ; Li, Qiongling ; Neitzke, Andrew ; Pozzetti, Beatrice ; Wienhard, Anna
Date(s) 19/05/2025 - 27/05/2025
URL associée https://indico.math.cnrs.fr/event/11569/
12 20

Holonomies of maximal globally hyperbolic Cauchy-compact conformally flat spacetimes

De Rym Smaï

$P_1$-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.

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