Equivariant and nonequivariant contact homology

I will discuss joint work with Hutchings which constructs nonequivariant anda family Floer equivariant version of contact homology. Both theories are generatedby two copies of each Reeb orbit over Z and capture interesting torsion information.We will see an obstruction bundle gluing correction term appear in the expression ofthe differential. I will then explain how one can recover the original cylindrical theoryproposed by Eliashberg-Givental-Hofer via our constructions.