Tori in certain aspherical four-manifolds

Some Examples of Aspherical Symplectic Four-manifolds

We give examples of aspherical symplectic 4-manifolds, which are formal in the sense of rational homotopy theory but have degenerate Lefschetz pairings. (preliminary version) Compact Kähler manifolds have a number of topological properties which are not shared by general symplectic manifolds, see [1] for example. In particular, Kähler manifolds have the following cohomological properties: 1. th...

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

Effective classes and Lagrangian tori in symplectic four-manifolds

An effective class in a closed symplectic four-manifold (X,ω) is a twodimensional homology class which is realized by a J-holomorphic cycle for every tamed almost complex structure J . We prove that effective classes are orthogonal to Lagrangian tori in H2(X;Z).