Roman Sauer: "Volume and macroscopic scalar curvature"

mardi 4 mai 2021, 10:15 → 11:15 Europe/Paris

Abstract: We prove the macroscopic cousins of three conjectures:

1) a conjectural bound of the simplicial volume of a Riemannian manifold in the presence of a lower scalar curvature bound,

2) the conjecture that rationally essential manifolds do not admit metrics of positive scalar curvature,

3) a conjectural bound of l2-Betti numbers of aspherical Riemannian manifolds in the presence of a lower scalar curvature bound.

The macroscopic cousin is the statement one obtains by replacing a lower scalar curvature bound by an upper bound on the volumes of $1$-balls in the universal cover. Group actions on Cantor spaces surprisingly play an important role in the proof. The talk is based on joint work with Sabine Braun.