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February 2013 Minimal models, formality, and hard Lefschetz properties of solvmanifolds with local systems
Hisashi Kasuya
J. Differential Geom. 93(2): 269-297 (February 2013). DOI: 10.4310/jdg/1361800867

Abstract

For a simply connected solvable Lie group $G$ with a cocompact discrete subgroup $\Gamma$, we consider the space of differential forms on the solvmanifold $G/\Gamma$ with values in a certain flat bundle so that this space has a structure of a differential graded algebra (DGA). We construct Sullivan’s minimal model of this DGA. This result is an extension of Nomizu’s theorem for ordinary coefficients in the nilpotent case. By using this result, we refine Hasegawa’s result of formality of nilmanifolds and Benson-Gordon’s result of hard Lefschetz properties of nilmanifolds.

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Hisashi Kasuya. "Minimal models, formality, and hard Lefschetz properties of solvmanifolds with local systems." J. Differential Geom. 93 (2) 269 - 297, February 2013. https://doi.org/10.4310/jdg/1361800867

Information

Published: February 2013
First available in Project Euclid: 25 February 2013

zbMATH: 1373.53069
MathSciNet: MR3024307
Digital Object Identifier: 10.4310/jdg/1361800867

Rights: Copyright © 2013 Lehigh University

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Vol.93 • No. 2 • February 2013
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