关于微分同胚的一个充分必要条件(英文)

A Necessary and Sufficient Condition on Diffeomorphisms

确定两个流形是否微分同胚是微分流形研究中的重要课题，本文定义了反层的概念，给出了反层范畴，由此找到两个微分流形，Ｃ微分同胚的特征刻画，于是给出了一种较以往更优的判定法．

We introduce anti-sheaves for Cr-manifolds and a category of anti-sheaves. The adjoint equivalence between the category of anti-sheaves and the category of manifolds is established. Using such an equivalence, we obtain a characterization for deciding whether two given manifolds arc Cr-diffeomorphic in terms of inherent W.(G)- sheaves. This provides the first known criterion for determining whether two given man- ifolds are diffeomorphic.