Leonardo Macarini, Universidade Federal do Rio de Janeiro
Cylindrical contact homology of even contact forms
Cylindrical contact homology is a powerful invariant of contact structures introduced by Eliashberg, Givental and Hofer in the bigger setup of Symplectic Field Theory. Although it resembles a Floer homology for the action functional induced by the contact form, it has several differences to the Floer homology of monotone symplectic manifolds. Indeed, it is not defined for any contact form and Eliashberg, Givental and Hofer proved that it is well defined and an invariant of the contact structure under some rather restrictive hypotheses on the contact form. We prove an extension of their result to even contact forms, that is, contact forms whose Reeb flow has no periodic orbit of odd degree. A large class of examples of these forms is given by toric contact manifolds whose cylindrical contact homology can be combinatorially computed in terms of the associated momentum cone. This is joint work with Miguel Abreu.