no. 6
Mixed Hodge structures and Sullivan’s minimal models of Sasakian manifolds
Kasuya, Hisashi1
1 Department of Mathematics Graduate School of Science Osaka University, Osaka (Japan)
Annales de l'Institut Fourier, Volume 67 (2017) no. 6, pp. 2533-2546.

We show that the Malčev Lie algebra of the fundamental group of a compact 2n+1-dimensional Sasakian manifold with n≥2 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.

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 n≥2. 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.

Received:
Revised:
Accepted:
Published online:
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)
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Kasuya, Hisashi. Mixed Hodge structures and Sullivan’s minimal models of Sasakian manifolds. Annales de l'Institut Fourier, Volume 67 (2017) no. 6, pp. 2533-2546. doi : 10.5802/aif.3142. https://aif.centre-mersenne.org/articles/10.5802/aif.3142/

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