Flat bundles and Hyper-Hodge decomposition on solvmanifolds
Hisashi Kasuya
TL;DR
This paper investigates rank 1 flat bundles on solvmanifolds, utilizing Hodge theory to extend known structure theorems for Kähler solvmanifolds, and provides new insights into their cohomological properties.
Contribution
It offers a new representation of the structure theorem for Kähler solvmanifolds by applying Hodge theoretical properties to flat bundles, extending previous results for nilmanifolds.
Findings
Representation of Kähler solvmanifolds as extensions
Hodge theoretical properties for flat bundles
Extension of results from nilmanifolds to solvmanifolds
Abstract
We study rank flat bundles over solvmanifolds whose cohomologies are non-trivial. By using Hodge theoretical properties for all topologically trivial rank 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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology