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On the structure of finite-sheeted coverings of compact connected groups

S. A. Grigorian·R. N. Gumerov
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Abstract

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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S. A. Grigorian, R. N. Gumerov. 2004-03-20. On the structure of finite-sheeted coverings of compact connected groups. https://arxiv.org/abs/math/0403329

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