Flat bundles and Hyper-Hodge decomposition on solvmanifolds

Abstract

We study rank $1$ flat bundles over solvmanifolds whose cohomologies are non-trivial. By using Hodge theoretical properties for all topologically trivial rank $1$ flat bundles, we represent the structure theorem of Kähler solvmanifolds as extensions of Hasegawa's result and Benson-Gordon's result for nilmanifolds.

To appear in Int. Math. Res. Not. IMRN

References in corpus (3)

• The cohomologies of the Iwasawa manifold and of its small deformations
• Geometry of nilmanifolds with left-invariant complex structure and deformations in the large
• Characteristic varieties of nilpotent groups and applications

Cited by in corpus (2)

• Hodge theory for twisted differentials
• Cohomologies of Sasakian groups and Sasakian solvmanifolds