Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds

Hisashi Kasuya

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arXiv · 2007.14544

Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds

Hisashi Kasuya

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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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BibTeX RIS

Hisashi Kasuya. 2020-07-29. Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds. https://arxiv.org/abs/2007.14544

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