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We express the rational cohomology of the unordered configuration space of acompact oriented manifold as a representation of its mapping class group interms of a weight-decomposition of the rational cohomology of the mapping spacefrom the manifold to a sphere. We apply this to the case of a compact orientedsurface with one boundary component and explicitly compute the rationalcohomology of its unordered configuration space as a representation of itsmapping class group. In particular, this representation is not symplectic, buthas trivial action of the second Johnson filtration subgroup of the mappingclass group.

Cohomology of configuration spaces of surfaces as mapping class group representations