Skip to main content
Log in

On Covering Groups

  • Brief Communications
  • Published:
Russian Mathematics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Pontryagin, L.S. Continuous groups (Nauka, Moscow, 1984) [in Russian].

    MATH  Google Scholar 

  2. 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).

    MathSciNet  MATH  Google Scholar 

  3. Clark, A. “A generalization of Hagopian’s theorem and exponents”, Topol. Appl. 117 (3), 273–283 (2002).

    Article  MathSciNet  Google Scholar 

  4. Grigorian, S.A., Gumerov, R.N. “On a covering group theorem and its applications”, Lobachevskii J. Math. 10, 9–16 (2002).

    MathSciNet  MATH  Google Scholar 

  5. 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].

    Google Scholar 

  6. Gumerov, R.N. “On finite-sheeted covering mappings onto solenoids”, Proc. Amer. Math. Soc. 133 (9), 2771–2778 (2005).

    Article  MathSciNet  Google Scholar 

  7. Gumerov, R.N. “On the existence of means on solenoids”, Lobachevskii J. Math. 17, 43–46 (2005).

    MathSciNet  MATH  Google Scholar 

  8. Eda, K., Matijević, V. “Finite-sheeted covering maps over 2-dimensional connected, compact Abelian groups”, Topology Appl. 153 (7), 1033–1045 (2006).

    Article  MathSciNet  Google Scholar 

  9. Grigorian, S.A., Gumerov, R.N. “On the structure of finite coverings of compact connected groups”, Topology Appl. 153 (18), 3598–3614 (2006).

    Article  MathSciNet  Google Scholar 

  10. Eda, K., Matijević, V. “Covering maps over solenoids which are not covering homomorphisms”, Fund. Math. 221 (1), 69–82 (2013).

    Article  MathSciNet  Google Scholar 

  11. Gumerov, R.N. “Weierstrass polynomials and coverings of compact groups”, Sib. Math. J. 54 (2), 213–216 (2013).

    Article  MathSciNet  Google Scholar 

  12. Gumerov, R.N. “Characters and coverings of compact groups”, Russ. Math. (IzvVUZ) 4, 7–13 (2014).

    Article  MathSciNet  Google Scholar 

  13. Dydak, J. “Overlays and group actions”, Topology Appl. 207, 22–32 (2016).

    Article  MathSciNet  Google Scholar 

  14. Eda, K., Matijević, V. “Existence and uniqueness of group structures on covering spaces over groups”, Fund. Math. 238 (3), 241–267 (2017).

    Article  MathSciNet  Google Scholar 

  15. 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).

    MathSciNet  Google Scholar 

  16. Gumerov, R.N. “Limit automorphisms of C*-algebras generated by isometric representations for semigroups of rationals”, Sib. Math. J. 59 (1), 73–84 (2018).

    Article  MathSciNet  Google Scholar 

  17. Bohr, H., Flanders, D.A. “Algebraic equations with almost-periodic coefficients”, Kgl. Danske Videnskabernes Selskab. Mathematisk-fysiske Meddelelser. 15, 1–49 (1937).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. N. Gumerov.

Additional information

Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 3, pp. 85–91.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gumerov, R.N. On Covering Groups. Russ Math. 64, 76–81 (2020). https://doi.org/10.3103/S1066369X20030081

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1066369X20030081

Key words

Navigation