English

On the de Rham cohomology of solvmanifolds

Differential Geometry 2009-12-11 v1

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 GG by a lattice Γ\Gamma. This result can be applied to compute the Betti numbers of a compact solvmanifold G/ΓG/\Gamma even in the case that the solvable Lie group GG and the lattice Γ\Gamma do not satisfy the Mostow condition.

Keywords

Cite

@article{arxiv.0912.2006,
  title  = {On the de Rham cohomology of solvmanifolds},
  author = {Sergio Console and Anna Fino},
  journal= {arXiv preprint arXiv:0912.2006},
  year   = {2009}
}

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15 pages