Topology of Properly Convex Projective Manifolds of Dimension Four (and Higher)

par Andrea Seppi (Università di Torino)

lundi 8 déc. 2025, 14:00 → 15:15 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

I will present several results on the topology of closed manifolds of dimension at least 4 that admit a (real) properly convex projective structure, all related to a vanishing theorem of Kobayashi from 1984 for the rational Pontryagin classes. In arbitrary dimensions, I will outline a classification of locally symmetric manifolds admitting properly convex projective structures. Focusing on dimension 4, I will then present a result on the geometric decomposition which is the analogue of a theorem of Benoist in dimension 3, and the construction of examples that realize all possible positive values of the Euler characteristic. Based on joint work with Stefano Riolo and Leone Slavich.