论文标题
符号平坦和扭曲的原始共同体学
Symplectic Flatness and Twisted Primitive Cohomology
论文作者
论文摘要
我们介绍了与象征流形的连接和纤维束的符号平坦的概念。给定$ a_ \ infty $ -Algebra，我们提出了一种平坦的条件，可以使与$ a_ \ infty $ -Algebra相关的微分复合物的扭曲。符号平坦的条件是由Tsai，Tseng和Yau构建的差异形式的$ a_ \ infty $ algebra产生的。当符号歧管配备兼容度量时，符号扁平连接代表了Yang-Mills连接的特殊子类。我们进一步研究了扭曲的差分复合物的共同体，并为它们提供了简单的消失定理。
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.
