标题： 在全局亚解析设定中的德拉姆定理 显示英文标题

标题： On the de Rham theorem in the globally subanalytic setting

摘要： 对于全局子解析流形，我们定义了全局子解析微分形式的德拉姆复形和可构造微分形式的德拉姆复形。 尽管在非紧的情况下，前者的德拉姆定理不成立，但后者的德拉姆上同调群在完全一般的情况下成立。 我们推导出可构造的德拉姆上同调群与经典上同调群是典范同构的。 我们强调，我们的结果已经适用于$C^1$的情形。 显示英文摘要

摘要： For globally subanalytic manifolds we define de Rham complexes of globally subanalytic differential forms and of constructible differential forms. Whereas the de Rham theorem does not hold for the former in the non-compact case, it does hold for the latter in full generality. We deduce that the constructible de Rham cohomology groups are canonically isomorphic to the classical ones. We stress that our results apply already in the $C^1$-setting.