A quantum Leray–Hirsch theorem for banded gerbes

Abstract

For a gerbe $\mathcal{Y}$ over a smooth proper Deligne–Mumford stack $\mathcal{B}$ banded by a finite group $G$, we prove a structure result on the Gromov–Witten theory of $\mathcal{Y}$, expressing Gromov–Witten invariants of $\mathcal{Y}$ in terms of Gromov–Witten invariants of $\mathcal{B}$ twisted by various flat $U(1)$‑gerbes on $\mathcal{B}$. This can be viewed as a Leray–Hirsch type of result for Gromov–Witten theory of gerbes.