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?