On the de Rham cohomology of solvmanifolds

2009/12/10 by Sergio Console, Console, Sergio, Anna Fino +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:22E25 #msc:22E40 #msc:53C30

paper · pdf · doi:10.48550/arxiv.0912.2006

15 pages

arxiv created 2009/12/10 · arxiv updated 2010/01/07

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

Citations

• A Pseudo-Kähler Structure on a Nontoral Compact Complex Parallelizable Solvmanifold

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