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

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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.
18 pages

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General Topology, 57M10, 54C10, 54H11, 22C05

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http://salesiana.dossiersoluciones.com/handle/123456789/70517

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0403329
 http://arxiv.org/abs/math/0403329

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arXiv