Smoothness of Kuranishi atlases on Gromov-Witten moduli spaces

Abstract: Kuranishi atlases were introduced by McDuff and Wehrheim to build a virtual fundamental class on moduli spaces of J-holomorphic curves and resolve some of the challenges in this field. This paper considers Gromov-Witten moduli spaces and shows they admit a smooth enough Kuranishi atlas to be able to define a Gromov-Witten virtual fundamental class in any virtual dimension. The key step for this result is the proof of a stronger gluing theorem.