Genus zero Gromov-Witten axioms via Kuranishi atlases

Abstract

A Kuranishi atlas is a structure used to build a virtual fundamental class on moduli spaces of $J$-holomorphic curves. They were introduced by McDuff and Wehrheim to resolve some of the challenges in this field. This paper completes the construction of genus zero Gromov-Witten invariants using Kuranishi atlases and proves the Gromov-Witten axioms of Kontsevich and Manin. To do so, we introduce the notion of a transverse subatlas, a useful tool for working with Kuranishi atlases.