Mixed Hodge structures and Sullivan's minimal models of Sasakian manifolds

TL;DR

This paper demonstrates that the Malcev Lie algebra of a compact Sasakian manifold's fundamental group admits a quadratic presentation, utilizing bigradings of minimal models of mixed-Hodge diagrams, and simplifies related proofs.

Contribution

It introduces a new approach using bigradings of minimal models to analyze the Malcev Lie algebra of Sasakian manifolds, providing a simplified proof of existing results.

Findings

Malcev Lie algebra admits quadratic presentation for certain Sasakian manifolds

Utilizes Morgan's bigradings of minimal models of mixed-Hodge diagrams

Simplifies proof of previous results on Sasakian nilmanifolds

Abstract

We show that the Malcev Lie algebra of the fundamental group of a compact $2n+1$-dimensional Sasakian manifold with $n\ge 2$ 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.