Quantum type cohomologies on contact manifolds

Abstract

We extend the notion of a pseudoholomorphic map in a symplectic manifold to the one of an almost coholomorphic map on a contact manifold M of an odd dimension. We study the moduli space of stable almost coholomorphic maps that represent a two-dimensional integral homology class of M, Gromov-Witten type invariants, quantum type products and quantum type cohomologies. © 2013 World Scientific Publishing Company.