Gromov-Witten theory of product stacks

Understand

Let $\mathcal{X}_1$ and $\mathcal{X}_2$ be smooth proper Deligne-Mumford stacks with projective coarse moduli spaces.

• We prove a formula for orbifold Gromov-Witten invariants of the product stack $\mathcal{X}_1\times \mathcal{X}_2$ in terms of Gromov-Witten invariants of the factors $\mathcal{X}_1$ and $\mathcal{X}_2$.
• As an application, we deduce a decomposition result for Gromov-Witten theory of trivial gerbes.