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We give necessary conditions for the existence of a compact manifold locallymodelled on a given homogeneous space, which generalize some earlier results,in terms of relative Lie algebra cohomology. Applications include bothreductive and nonreductive cases. For example, we prove that there does notexist a compact manifold locally modelled on a positive dimensional coadjointorbit of a real linear solvable algebraic group.

Homogeneous spaces of nonreductive type locally modelling no compact manifold