Georgia Institute of Technology College of Sciences

We discuss two concepts of low-dimensional topology in higher dimensions: near-symplectic manifolds and overtwisted contact structures. We present a generalization of near-symplectic 4-manifolds to dimension 6. By near-symplectic, we understand a closed 2-form that is symplectic outside a small submanifold where it degenerates. This approach uses some singular mappings called generalized broken Lefschetz fibrations. An application of this setting appears in contact topology. We find that a contact 5-manifold, which appears naturally in this context, is PS-overtwisted. This property can be detected in a rather simple way.