Geodesic
On a~covering group theorem and its applications
Lobachevskii journal of mathematics, Tome 10 (2002), pp. 9-16.

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Let $p\colon X\to G$ be an n-fold covering of a compact group $G$ by a connected topological space $X$ Then there exists a group structure in $X$ turning $p$ into a homomorphism between compact groups. As an application, we describe all $n$-fold coverings of a compact connected abelian group. Also, a criterion of triviality for $n$-fold coverings in terms of the dual group and the one-dimensional Čech cohomology group is obtained.
Keywords: $n$-fold coverings of compact groups, covering groups, algebraic coverings, criterion of triviality forfunction $n$-fold coverings, dual group, onedimensional Čech cohomology group, algebraic equations with coefficients in function algebras. 
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S. A. Grigoryan; R. N. Gumerov. On a~covering group theorem and its applications. Lobachevskii journal of mathematics, Tome 10 (2002), pp. 9-16. http://geodesic.mathdoc.fr/item/LJM_2002_10_a1/

[AS] R. Arens, I. Singer, “Generalized analytic functions”, Trans. Amer. Math. Soc., 81 (1956), 379–393 | DOI | MR | Zbl

[Bo] H. Bohr, “Über fastperiodische ebene Bewegungen”, Comm. Math. Helv., 4 (1932), 51–64 | DOI | MR | Zbl

[Br] N. Bruschlinsky, “Stetige Abbildungen und Bettische Gruppen der Dimensionzahl 1 und 3”, Math. Ann., 109 (1934), 525–537 | DOI | MR | Zbl

[BF] H. Bohr, D. A. Flanders, 7, Kobenhavn, 1937

[Ei] S. Eilenberg, “Transformations continues en circonférence et la topologie du plan”, Fund Math., 26 (1936), 61–112 | Zbl

[En] R. Engelking, General Topology, Warszawa, 1977 | MR

[ES] S. Eilenberg, N. Steenrod, Foundations of Algebraic Topology, Princeton Univ. Press, New Jersey, 1952 | MR | Zbl

[F] O. Forster, Riemannsche Flächen, Heidelberger Taschenbücher Band, 184, Springer-Verlag, New York, 1977 | MR | Zbl

[G] T. W. Gamelin, Uniform Algebras, Prentice-Hall Series in Modern Analysis, N.J., 1969 | MR

[Go1] Math. USSR, Sb., 11 (1970), 233–243 | DOI | MR | Zbl

[Go2] Sov. Math. Dokl., 12 (1971), 1371–1375 | MR | Zbl

[GL] Math. USSR, Sb., 7 (1969), 569–596 | DOI | MR | Zbl

[Gr] S. A. Grigorian, “Generalized analytic functions”, Uspekhi Mat. Nauk, 49:2 (1996), 3–42 (in Russian) | MR

[GGK1] S. A. Grigorian, R. N. Gumerov, A. V. Kazantsev, “Group structure in finite coverings of compact solenoidal groups”, Lobachevskii Journal of Mathematics, VI (2000), 39–46 | MR

[GGK2] S. A. Grigorian, R. N. Gumerov, A. V. Kazantsev, “Unramified coverings of solenoidal groups and the Bohr–Walter–Flanders theorem” (to appear) (in Russian)

[HR] E. Hewitt, K. A. Ross, Abstract Harmonic Analysis, Vol. 1, Springer, Berlin, 1963 | Zbl

[vK] E. R. van Kampen, “On almost periodic functions of constant absolute value”, J. London Math. Soc., XII:1 (1937), 3–6

[M] W. S. Massey, Algebraic Topology: An Introduction, Harcourt, Brace World, Inc., New York, 1967 | MR | Zbl

[P] L. S. Pontrjagin, Continuous groups, Nauka, Moscow, 1984 (in Russian) | MR

[R] H. Royden, “Function Algebras”, Bull. Amer. Math. Soc., 69:3 (1963), 281–298 | DOI | MR | Zbl

[Wa] A. Walter, “Algebraishe Funtionen von fastperiodischen Funktionen”, Monatsh. Math. und Phys., 40:2 (1933), 444–457 | DOI | MR

[We] A. Weil, L'intégration dans les groupes topologiques et ses applications, Paris, 1940