On the de Rham cohomology of solvmanifolds

Details On the de Rham cohomology of solvmanifolds On the de Rham cohomology of solvmanifolds

2009-12-10

arxiv.org/abs/0912.2006v1

Mathematics

Differential Geometry

15 pages

Scientific paper

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.

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