Topological Rigidity for Non-aspherical Manifolds

Topological rigidity for non-aspherical manifolds by

The Borel Conjecture predicts that closed aspherical manifolds are topological rigid. We want to investigate when a non-aspherical oriented connected closed manifold M is topological rigid in the following sense. If f : N → M is an orientation preserving homotopy equivalence with a closed oriented manifold as target, then there is an orientation preserving homeomorphism h : N → M such that h an...

Topological Rigidity for Hyperbolic Manifolds

Let M be a complete Riemannian manifold having constant sectional curvature —1 and finite volume. Let M denote its Gromov-Margulis manifold compactification and assume that the dimension of M is greater than 5. (If M is compact, then M = M and dM is empty.) We announce (among other results) that any homotopy equivalence h: (N,dN) —• (M,dM), where N is a compact manifold, is homotopic to a homeo...

Aspherical Manifolds*

This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions. The property aspherical, which is a purely homotopy theoretical condition, has many striking implications about the geometry and analysis of the manifold or ...

Survey on Aspherical Manifolds

This is a survey on known results and open problems about closed aspherical manifolds, i.e., connected closed manifolds whose universal coverings are contractible. Many examples come from certain kinds of non-positive curvature conditions. The property aspherical, which is a purely homotopy theoretical condition, implies many striking results about the geometry and analysis of the manifold or i...

Exotic aspherical manifolds