Gradient invariants of aspherical manifolds with small amenable multiplicity

Virtual talk.

If an oriented closed connected aspherical manifold admits an open amenable cover of ``small'' multiplicity, then the rank gradient, the \(\ell^2\)-Betti numbers and the torsion homology gradients of its fundamental group are all zero. This phenomenon admits a uniform proof via a dynamical version of simplicial volume. In this talk, I will survey this method as well as related results on 3-manifolds. This is based on joint work with Marco Moraschini and Roman Sauer.