Nash流形上Schwartz函数的De-Rham定理和Shapiro引理
De-Rham theorem and Shapiro lemma for Schwartz functions on Nash manifolds
摘要：
在本文中，我们继续我们的工作施瓦茨函数和广义施瓦茨函数的纳什（即光滑半代数）流形。我们的第一个目标是证明类似的de-Rham定理的de-Rham复系数的Schwartz函数和广义Schwartz函数。利用它计算了G-传递簇M上G-等变丛的广义Schwartz截面空间中系数的代数群G的李代数的上同调。我们是在G和M的拓扑性质的一些假设下进行的。经典情况下的这种计算被称为夏皮罗引理。
英文摘要：
In this paper we continue our work on Schwartz functions and generalized Schwartz functions on Nash (i.e. smooth semi-algebraic) manifolds. Our first goal is to prove analogs of de-Rham theorem for de-Rham complexes with coefficients in Schwartz functions and generalized Schwartz functions. Using that we compute cohomologies of the Lie algebra of an algebraic group G with coefficients in the space of generalized Schwartz sections of G-equivariant bundle over a G-transitive variety M. We do it under some assumptions on topological properties of G and M. This computation for the classical case is known as Shapiro lemma.
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