Holomorphic curves in symplectizations

We will say something about "Contact Homology," an invariant of contact manifolds in the spirit of Floer homology. This and related invariants can be compared between "symplectically cobordant" contact manifolds, leading to the notion of "Symplectic Field Theory."

Both the definition of the invariant itself and the action on cobordisms require the consideration of holomorphic curves in symplectic manifolds with cylindrical ends, which is an interesting business.