关于紧连通群的有限片覆盖的结构
On the structure of finite-sheeted coverings of compact connected groups
摘要：
研究了紧连通群上的单片覆盖映射。证明了从连通Hausdorff拓扑空间到紧连通阿贝尔群G的有限单覆盖映射必是同胚的，只要G的特征群允许按给定覆盖映射的度除.利用这一结果，我们得到了G的有限覆盖的平凡性的判别准则。为了证明这些事实，对于从紧拓扑空间到紧连通群的k-单覆盖映射，我们构造了一个李群上的k-单覆盖的逆系统，它逼近这个覆盖映射，并证明了一个覆叠群定理.
英文摘要：
Finite-sheeted covering mappings onto compact connected groups are studied. It is shown that a finite-sheeted covering mapping from a connected Hausdorff topological space onto a compact connected abelian group G must be a homeomorphism provided that the character group of G admits division by the degree of given covering mapping. Using this result, we obtain criteria of triviality for finite coverings of G in terms of its character group and means on G. In order to establish these facts, for a k-sheeted covering mapping from a compact topological space onto a compact connected group, we construct an inverse system of k-sheeted coverings onto Lie groups which approximates this covering mapping and prove a covering group theorem.
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