Abstract
We study finite-sheeted covering mappings from compact connected spaces onto compact connected groups. For such a covering mapping we consider a method of supplying its covering space by a group structure. The covering space endowed with that group structure is a topological group, and a given covering mapping turns into a homomorphism of compact connected groups.
References
Pontryagin, L.S. Continuous groups (Nauka, Moscow, 1984) [in Russian].
Grigorian, S.A., Gumerov, R.N., Kazantsev, A.V. “Group structure in finite coverings of compact solenoidal groups”, Lobachevskii J. Math. 6, 39–46 (2000).
Clark, A. “A generalization of Hagopian’s theorem and exponents”, Topol. Appl. 117 (3), 273–283 (2002).
Grigorian, S.A., Gumerov, R.N. “On a covering group theorem and its applications”, Lobachevskii J. Math. 10, 9–16 (2002).
Bogatyi, S.A., Frolkina, O.D. “Classification of generalized solenoids” (in: Tr. sem. on vector and tensor analysis with their appl. to geom., mech. and phys. XXVI, pp. 31–59 (Izd-vo MGU, Moscow, 2005)) [in Russian].
Gumerov, R.N. “On finite-sheeted covering mappings onto solenoids”, Proc. Amer. Math. Soc. 133 (9), 2771–2778 (2005).
Gumerov, R.N. “On the existence of means on solenoids”, Lobachevskii J. Math. 17, 43–46 (2005).
Eda, K., Matijević, V. “Finite-sheeted covering maps over 2-dimensional connected, compact Abelian groups”, Topology Appl. 153 (7), 1033–1045 (2006).
Grigorian, S.A., Gumerov, R.N. “On the structure of finite coverings of compact connected groups”, Topology Appl. 153 (18), 3598–3614 (2006).
Eda, K., Matijević, V. “Covering maps over solenoids which are not covering homomorphisms”, Fund. Math. 221 (1), 69–82 (2013).
Gumerov, R.N. “Weierstrass polynomials and coverings of compact groups”, Sib. Math. J. 54 (2), 213–216 (2013).
Gumerov, R.N. “Characters and coverings of compact groups”, Russ. Math. (IzvVUZ) 4, 7–13 (2014).
Dydak, J. “Overlays and group actions”, Topology Appl. 207, 22–32 (2016).
Eda, K., Matijević, V. “Existence and uniqueness of group structures on covering spaces over groups”, Fund. Math. 238 (3), 241–267 (2017).
Gumerov, R.N. “Coverings of solenoids and automorphisms of semigroup C*-algebras”, Uchenye Zapiski Kazanskogo Universiteta. Seria Fiziko-Matem. Nauki 160 (2), 275–286 (2018).
Gumerov, R.N. “Limit automorphisms of C*-algebras generated by isometric representations for semigroups of rationals”, Sib. Math. J. 59 (1), 73–84 (2018).
Bohr, H., Flanders, D.A. “Algebraic equations with almost-periodic coefficients”, Kgl. Danske Videnskabernes Selskab. Mathematisk-fysiske Meddelelser. 15, 1–49 (1937).
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Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 3, pp. 85–91.
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Gumerov, R.N. On Covering Groups. Russ Math. 64, 76–81 (2020). https://doi.org/10.3103/S1066369X20030081
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DOI: https://doi.org/10.3103/S1066369X20030081