Appears in collection : Not Only Scalar Curvature Seminar

Scalar curvature encodes the volume information of small geodesic balls within a Riemannian manifold, making it, to some extent, the weakest curvature invariant. This raises a natural question: what topological constraints does scalar curvature impose on manifolds? In this talk, we shall show that for a manifold with a scalar curvature lower bound (possibly negative), the simplicial norm of the Poincaré dual of the A-hat class can be controlled. This is joint work with Guoliang Yu.