Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds
Almost-formality and deformations of representations of the fundamental groups of Sasakian manifolds
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Sasakian流形基本群表示的近形式化和变形
DOI：
10.1007/s10231-023-01301-6
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
Kasuya Hisashi
中科院分区：
文献类型：
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作者：
Kasuya Hisashi
对于a维紧Sasakian流形，我们证明了基本群在每个半单表示下的各种表示的解析芽是二次的。为了证明这一结果，我们证明了取值于半单平坦向量丛的Sasakian流形的De Rham复形的几乎正式性。利用几乎形式化证明了紧Sasakian流形上半单平坦向量丛的上同调的杯积的零化定理。
For a-dimensional compact Sasakian manifold, if, 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.