10. Mai 2022
Christoforos Neofytidis (Ohio State University)
Aspherical manifolds and endomorphisms of their fundamental groups
The Borel conjecture asserts that the homeomorphism type of a closed aspherical manifold is determined by its fundamental group. Manifolds satisfying the Borel conjecture are called topologically rigid. In this talk, we generalize in all dimensions (and give a new, uniform proof of) a rigidity theorem on aspherical fibered 3-manifolds, due to Gromov, Thurston and Wang. A key ingredient for this new, mostly algebraic, approach is the non-vanishing of the Euler characteristic of the fiber (which is a hyperbolic surface in dimension three). We then explain how the Euler characteristic is expected to determine the topology of aspherical manifolds with respect to the Borel conjecture, as well as other long-standing problems, such as the Hopf problem in Topology and the Anosov-Smale conjecture in Dynamics.