Cari colleghi, vi segnalo che giovedi' 18 giugno alle 14:30 in aula seminari ci sara' un seminario di geometria. Trovate qui sotto titolo e abstract. Per chi fosse interessato, ci troviamo nell'atrio davanti all'aula Riunioni alle 13 per andare a pranzo con lo speaker. Saluti, Andrea
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Titolo: Simplicial volume of real convex projective manifolds
Speaker: Grazia Rago (Università di Bologna) Abstract: A real convex projective manifold is a (RP^d, PGL(d+1,R))-structure where the developing map's image is a properly convex domain Ω⊂RP^d and the holonomy group is a discrete, torsion-free subgroup Γ≤ PGL(d+1,R) preserving Ω. In this talk, we analyze the simplicial volume of a closed real convex projective manifold M≅Ω/Γ. We introduce the flat-rank of a properly convex domain and we show that if the flat-rank of Ω is 1, then ∥M∥>0. On the other hand, we present also examples where the flat-rank is greater than 1 and the simplicial volume is positive. To conclude, we relate the simplicial volume to the Euler characteristic, affirmatively answering a famous question by Gromov in this setting: if the simplicial volume of a closed aspherical manifold vanishes, must its Euler characteristic vanish as well?
