Towards quantum cohomology of real varieties

Abstract

This paper is devoted to a discussion of Gromov-Witten-Welschinger (GWW) classes and their applications. In particular, Horava's definition of quantum cohomology of real algebraic varieties is revisited by using GWW-classes and it is introduced as a DG-operad. In light of this definition, we speculate about mirror symmetry for real varieties.