Geometric Properties of Real Gromov-Witten Invariants

Abstract: We collect geometric properties of the all-genus real Gromov-Witten theory and provide updates on its development since its introduction in 2015. We bring attention to a modification of the original construction of this theory which is applicable in a broader setting, obtain properties of the orientations of the moduli spaces of real maps under this modification which had previously been obtained for the original construction, and compare such orientations obtained via the two constructions when both constructions are applicable. In particular, the orientation of the moduli space of real maps from a disjoint union of domains may not be the product orientation of the moduli spaces of real maps from its components, a possibility overlooked in our past work.