Symplectically aspherical manifolds

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...

Length Minimizing Hamiltonian Paths for Symplectically Aspherical Manifolds

In this paper we consider the length minimizing properties of Hamiltonian paths generated by quasi-autonomous Hamiltonians on symplectically aspherical manifolds. Motivated by the work of Schwarz in [Sc], we study the role of the fixed global extrema in the Floer complex of the generating Hamiltonian. Our main result determines a natural condition on a fixed global maximum of a Hamiltonian whic...

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