On the structure of finite coverings of compact connected groups |
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Authors: | SA Grigorian |
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Institution: | a Chair of Mathematics, Kazan State Power Engineering University, Krasnoselskaya 51, Kazan, 420066, Tatarstan, Russian Federation b Department of Mechanics and Mathematics, Kazan State University, Kremlevskaya 18, Kazan, 420008, Tatarstan, Russian Federation |
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Abstract: | Finite-sheeted covering mappings onto compact connected groups are studied. We show that for a covering mapping from a connected Hausdorff topological space onto a compact (in general, non-abelian) group there exists a topological group structure on the covering space such that the mapping becomes a homomorphism of groups. To prove this fact we construct an inverse system of covering mappings onto Lie groups which approximates the given covering mapping. As an application, it is shown that a covering mapping onto a compact connected abelian group G must be a homeomorphism provided that the character group of G admits division by degree of the mapping. We also get a criterion for triviality of coverings in terms of means and prove that each finite covering of G is equivalent to a polynomial covering. |
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Keywords: | 57M10 54C10 54H11 22C05 |
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