  We compute small rational models for configuration spaces of points on
oriented surfaces, as right modules over the framed little disks operad. We do
this by splitting these surfaces in unions of several handles. We first
describe rational models for the configuration spaces of these handles as
algebras in the category of right modules over the framed little disks operad.
We then express the configuration spaces of the surface as an "iterated
Hochschild complex" of these algebras with coefficients in the module given by
configurations in a sphere with holes.
  Physically, our results may be interpreted as saying that the partition
function of the Poisson-$\sigma$-model on closed surfaces has no quantum
corrections, i.e., no terms coming from Feynman diagrams of positive loop
order.
