Gromov-Witten invariants of BG and topological recursion
We shall show that the intersection numbers on the moduli space of stable morphisms from twisted curves to the classifying space of a finite group G satisfy a Eynard-Orantin topological recursion. We shall prove that counting a especial kind of designs drawn on an orbifold Riemann surface satisfies the a EO topological recursion with respect to the edge-removal operation and we will interpret this operation as a merging-spliting operation in terms of the product and coproduct on the Frobenius algebra defined by the orbifold cohomology of BG.