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An extention of Nomizu’s theorem – a user’s guide –. (English) Zbl 1351.22006
Summary: For a simply connected solvable Lie group \(G\) with a lattice \(\Gamma\), the author constructed an explicit finite-dimensional differential graded algebra \(A^\ast_\Gamma\) which computes the complex valued de Rham cohomology \(H^\ast(\Gamma\setminus G, \mathbb{C})\) of the solvmanifold \(\Gamma\setminus G\). In this note, we give a quick introduction to the construction of such \(A^\ast_\Gamma\) including a simple proof of \(H^\ast(A^\ast_\Gamma)\cong H^\ast(\Gamma\setminus G, \mathbb{C})\).

MSC:
22E25 Nilpotent and solvable Lie groups
22E40 Discrete subgroups of Lie groups
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