Abstract
For a \(2n+1\)-dimensional compact Sasakian manifold, if \(n\ge 2\), we prove that the analytic germ of the variety of representations of the fundamental group at every semi-simple representation is quadratic. To prove this result, we prove the almost-formality of de Rham complex of a Sasakian manifold with values in a semi-simple flat vector bundle. By the almost-formality, we also prove the vanishing theorem on the cup product of the cohomology of semi-simple flat vector bundles over a compact Sasakian manifold.
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Kasuya, H. Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds. Annali di Matematica 202, 1793–1801 (2023). https://doi.org/10.1007/s10231-023-01301-6
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DOI: https://doi.org/10.1007/s10231-023-01301-6