Hodge theory for twisted differentials
Daniele Angella, Hisashi Kasuya
TL;DR
This paper explores Hodge theory and cohomologies for complex manifolds with twisted differentials, providing new obstructions and proofs related to Fujiki's class and solvmanifolds.
Contribution
It introduces novel cohomological obstructions and offers a Hodge-theoretical proof characterizing solvmanifolds in Fujiki's class.
Findings
New cohomological obstruction for Fujiki's class
Hodge-theoretical proof of solvmanifold characterization
Enhanced understanding of twisted differential cohomologies
Abstract
We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class of Fujiki. We give a Hodge-theoretical proof of the characterization of solvmanifolds in class of Fujiki, first proven by D. Arapura.
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