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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:
 2.2e+26 Nilpotent and solvable Lie groups 2.2e+41 Discrete subgroups of Lie groups
Keywords:
solvmanifold; cohomology
Full Text:
References:
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