Geometric Properties of Real Gromov-Witten Invariants

TL;DR

This paper reviews geometric properties of real Gromov-Witten invariants, introduces a broader construction, and analyzes orientation issues in moduli spaces, enhancing understanding of their geometric and topological features.

Contribution

It presents a modified construction of real Gromov-Witten theory applicable in broader settings and compares orientations of moduli spaces under different constructions.

Findings

Orientation of moduli spaces can differ from product orientations.

Modified construction extends applicability of real Gromov-Witten theory.

Comparison of orientations clarifies previous assumptions.

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.