Joint IAS/Princeton University Symplectic Geometry Seminar

We consider the problem of defining cylindrical contact homology, in the absence of contractible Reeb orbits, using "classical" methods. The main technical difficulty is failure of transversality of multiply covered cylinders. One can fix this difficulty by using \(S^1\)-dependent almost complex structures, but at the expense of introducing another difficulty which we will explain. We outline how fixing the latter difficulty ultimately leads to a different theory, an analogue of positive symplectic homology. This talk is intended to be part of a series of expository talks on the foundations of contact homology, but prerequisites should be minimal.