The Gromov-Witten axioms for symplectic manifolds via polyfold theory
arXiv:1912.13374
Abstract
Polyfold theory, as developed by Hofer, Wysocki, and Zehnder, is a relatively new approach to resolving transversality issues that arise in the study of -holomorphic curves in symplectic geometry. This approach has recently led to a well-defined Gromov-Witten invariant for -holomorphic curves of arbitrary genus, and for all closed symplectic manifolds. The Gromov-Witten axioms, as originally described by Kontsevich and Manin, give algebraic relationships between the Gromov-Witten invariants. In this paper, we prove the Gromov-Witten axioms for the polyfold Gromov-Witten invariants.