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Hodge theory for twisted differentials. (English) Zbl 1320.32027
Summary: We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class $$\mathcal C$$ of Fujiki. We give a Hodge-theoretical proof of the characterization of solvmanifolds in class $$\mathcal C$$ of Fujiki, first stated by D. Arapura.

##### MSC:
 32M10 Homogeneous complex manifolds 53C30 Differential geometry of homogeneous manifolds 58A14 Hodge theory in global analysis
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##### References:
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