Mixed Hodge structures and Sullivan’s minimal models of Sasakian manifolds
[Structures de Hodge mixtes et modèles minimaux de Sullivan des variétés sasakiennes]
Annales de l'Institut Fourier, Tome 67 (2017) no. 6, pp. 2533-2546.

Nous montrons, en utilisant les bigraduations de Morgan de modèles minimaux de diagrammes de Hodge, que l’algèbre de Lie de Malčev du groupe fondamental d’une variété sasakienne compacte de dimension 2n+1 admet une présentation quadratique pour n2. A l’aide de bigraduations de modèles minimaux, nous simplifions également la démonstration du résultat de Cappelletti–Montano, De Nicola, Marrero et Yudin sur les nilvariétés sasakiennes.

We show that the Malčev Lie algebra of the fundamental group of a compact 2n+1-dimensional Sasakian manifold with n2 admits a quadratic presentation by using Morgan’s bigradings of minimal models of mixed-Hodge diagrams. By using bigradings of minimal models, we also simplify the proof of the result of Cappelletti–Montano, De Nicola, Marrero and Yudin on Sasakian nilmanifolds.

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DOI : 10.5802/aif.3142
Classification : 53C25, 55P62, 58A14
Keywords: Sasakian structure, Sullivan’s minimal model, Morgan’s mixed Hodge diagram, formality
Mot clés : structure sasakienne, modèle minimal de Sullivan, diagramme de Hodge mixte de Morgan, formalité
Kasuya, Hisashi 1

1 Department of Mathematics Graduate School of Science Osaka University, Osaka (Japan)
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Kasuya, Hisashi. Mixed Hodge structures and Sullivan’s minimal models of Sasakian manifolds. Annales de l'Institut Fourier, Tome 67 (2017) no. 6, pp. 2533-2546. doi : 10.5802/aif.3142. http://archive.numdam.org/articles/10.5802/aif.3142/

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