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arXiv · 2208.12189

Symplectic Flatness and Twisted Primitive Cohomology

Li-Sheng Tseng·Jiawei Zhou
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Abstract

We introduce the notion of symplectic flatness for connections and fiber bundles over symplectic manifolds. Given an $A_\infty$-algebra, we present a flatness condition that enables the twisting of the differential complex associated with the $A_\infty$-algebra. The symplectic flatness condition arises from twisting the $A_\infty$-algebra of differential forms constructed by Tsai, Tseng and Yau. When the symplectic manifold is equipped with a compatible metric, the symplectic flat connections represent a special subclass of Yang-Mills connections. We further study the cohomologies of the twisted differential complex and give a simple vanishing theorem for them.

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Li-Sheng Tseng, Jiawei Zhou. 2022-08-25. Symplectic Flatness and Twisted Primitive Cohomology. https://doi.org/10.1007/s12220-022-01018-7

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