On the de Rham cohomology of solvmanifolds

Console, Sergio; Fino, Anna

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 4, pp. 801-818.

Using results by D. Witte [35] on the superigidity of lattices in solvable Lie groups we get a new proof of a recent remarkable result obtained by D. Guan [15] 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.

Classification : 53C30, 22E25, 22E40

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