Real Ruan-Tian Perturbations

Abstract

Ruan-Tian deformations of the Cauchy-Riemann operator enable a geometric definition of (standard) Gromov-Witten invariants of semi-positive symplectic manifolds in arbitrary genera. We describe an analogue of these deformations compatible with our recent construction of real Gromov-Witten invariants in arbitrary genera. Our approach avoids the need for an embedding of the universal curve into a smooth manifold and systematizes the deformation-obstruction setup behind constructions of Gromov-Witten invariants.