On the de Rham cohomology of solvmanifolds

Abstract

By using results by D. Witte on the superigidity of lattices in solvable Lie groups we get a different proof of a recent remarkable result obtained by D. Guan on the de Rham cohomology of a compact solvmanifold, i.e. of a quotient of a connected and simply connected solvable Lie group $G$ by a lattice $\Gamma$. This result can be applied to compute the Betti numbers of a compact solvmanifold $G/\Gamma$ even in the case that the solvable Lie group $G$ and the lattice $\Gamma$ do not satisfy the Mostow condition.