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 K\"ahler solvmanifolds as extensions of Hasegawa's result and Benson-Gordon's result for nilmanifolds.Comment: To appear in Int. Math. Res. Not. IMR