Strong rigidity for high dimensional analogues of hyperbolic 3-manifold groups

  • Tagungsort:

    Geb. 20.30, SR 1.067

  • Datum:

    17.12.2024

  • Referent:

    Christoforos Neofytidis

  • Zeit:

    14:00 Uhr

  • Abstract: Hyperbolic manifolds satisfy a very strong form of rigidity, namely, every self-map of non-zero degree of a closed hyperbolic manifold is homotopic to a homeomorphism (even more, to an isometry in dimensions greater than two). In dimension three, hyperbolic manifolds are finitely covered by a mapping torus of a hyperbolic surface. In particular, their fundamental groups are virtually fibered with trivial center. I will explain a high dimensional analogue of the above strong rigidity for fibered aspherical manifolds and for their fundamental groups. Whether high, odd dimensional closed hyperbolic manifolds fit into this context is an open problem. In particular, hyperbolic structures and their consequences (such as non-vanishing of the simplicial volume) cannot be used for high dimensional fibered manifolds. We will give a uniform treatment in all dimensions in terms of Hopf-type properties.