Rational Betti numbers of configuration spaces

We compute the rational Betti numbers of the configuration space Ck(M) of k points in an even-dimensional orientable closed manifold M and prove that these numbers depend only on the rational cohomology algebra of the manifold. We give also a formula for the Euler–Poincaré characteristic of Ck(M) in terms only of k, and of the Euler–Poincaré characteristic of M.