A TQFT of intersection numbers on moduli spaces of admissible covers

We construct a two-level weighted TQFT whose structure coefficents are equivariant intersection numbers on moduli spaces of admissible cov-ers. Such a structure is parallel (and strictly related) to the local Gromov-Witten theory of curves in [BP04]. We compute explicitly the theory us-ing techniques of localization on moduli spaces of admissible covers of a parametrized P1. The Frobenius Algebras we obtain are one parameter deformations of the class algebra of the symmetric group Sd. In certain special cases we are able to produce explicit closed formulas for such de-formations in terms of the representation theory of Sd