Flat bundles and Hyper-Hodge decomposition on solvmanifolds
classification
🧮 math.DG
math.CVmath.GT
keywords
bundlesflatsolvmanifoldsrankresultahlerbenson-gordoncohomologies
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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.
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