关于轨道褶皱上微分结构的唯一性
On uniqueness of differential structures on orbifolds
摘要：
已知对于每个$s$，每个${\rm C}^r$ -orbifold，$1\leq r\leq\infty$，具有相容的${\rm C}^s$ -微分结构，其中$r< s\leqω$ .证明了如果两个约化的${\rm C}^r$ -orbifolds，$2\leq r\leqω$，是${\rm C}^2$ -复纯的，则它们是${\rm C}^r$ -复纯的.由此可见，在约化的${\rm C}^r$ -orbifold上相容的${\rm C}^s$ -微分结构$2\leq r<s\leqω$，直到${\rm C}^s$ -单同态都是唯一的.
英文摘要：
It is known that every ${\rm C}^r$-orbifold, $1\leq r\leq\infty$, has a compatible ${\rm C}^s$-differential structure, for every $s$, where $r< s\leqω$. We prove that if two reduced ${\rm C}^r$-orbifolds, $2\leq r\leqω$, are ${\rm C}^2$-diffeomorphic, then they are ${\rm C}^r$-diffeomorphic. It follows that the compatible ${\rm C}^s$-differential structure on a reduced ${\rm C}^r$-orbifold, $2\leq r<s\leqω$, is unique up to a ${\rm C}^s$-diffeomorphism.
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