Closed aspherical manifolds with center

Closed Aspherical Manifolds with Center (to Frank Raymond, with friendship and admiration)

We show that in all dimensions > 7 there are closed aspherical manifolds whose fundamental groups have nontrivial center but do not possess any topological circle actions. This disproves a conjectured converse (proposed by Conner and Raymond) to a classical theorem of Borel.

On the Action Spectrum for Closed Symplectically Aspherical Manifolds

Symplectic homology is studied on closed symplectic manifolds where the class of the symplectic form and the first Chern class vanish on the second homotopy group. Critical values of the action functional are associated to cohomology classes of the manifold. Those lead to continuous sections in the action spectrum bundle. The action of the cohomology ring via the cap-action and the pants-produc...

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