Holomorphic Curves in Symplectic Cobordisms

Contact geometry is often called the "odd-dimensional cousin" of symplectic geometry, and there are many interesting problems that lie in the intersection of the two subjects. In this and the next chapter, we will discuss a few such problems that can be attacked with holomorphic curve methods, some of which take some noticeable inspiration from McDuff's results on rational and ruled symplectic 4-manifolds. Unlike previous chapters, our intention here is not to give a complete exposition, but rather to whet the reader's appetite and point to other sources for further reading. The subject of symplectic field theory, which emerges from this discussion as one of the natural tools to approach problems in contact topology, remains a subject of active research.