Higher genus Gromov–Witten invariants as genus zero invariants of symmetric products

Abstract

I prove a formula expressing the descendent genus $g$ Gromov-Witten invariants of a projective variety $X$ in terms of genus $0$ invariants of its symmetric product stack $S^{g+1}(X)$. When $X$ is a point, the latter are structure constants of the symmetric group, and we obtain a new way of calculating the Gromov-Witten invariants of a point.