关于微分流形的Hochschild-Kostant-Rosenberg定理
About the Hochschild-Kostant-Rosenberg theorem for differentiable manifolds
摘要：
在本说明中，它将提供一套技术，可以帮助人们理解证明的Hochschild-Kostant-Rosenberg定理的微分流形。给出了代数上的多重微分算子和多导子的精确定义，当代数是微分流形上的函数代数时，在坐标自由描述中，可以研究这些概念。同时，构造了多导子上的上积，它对应于多向量域上的楔积的（Hochschild）上同调.最后给出了上述定理的一个证明。
英文摘要：
In this notes it will be provided a set of techniques which can help one to understand the proof of the Hochschild-Kostant-Rosenberg theorem for differentiable manifolds. Precise definitions of multidiferential operators and polyderivations on an algebra are given, allowing to work on these concepts, when the algebra is an algebra of functions on a differentiable manifold, in a coordinate free description. Also, it will be constructed a cup product on polyderivations which corresponds on (Hochschild) cohomology to wedge product on multivector fields. At the end, a proof of the above mentioned theorem will be given.
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