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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 4, Pages 25–47
DOI: https://doi.org/10.26907/0021-3446-2021-4-25-47 (Mi ivm9664) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Coverings in the category of principal bundles

T. A. Gonchara, E. I. Yakovlevb

a Nizhniy Novgorod State University, 23 Ave. Gagarina, Nizhniy Novgorod, 603950 Russia
b International Laboratory of Dynamical Systems and Applications; National Research University Higher School of Economics, 25/12 Bolshaya Pecherskaya str., Nizhniy Novgorod, 603155 Russia
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DOI: https://doi.org/10.26907/0021-3446-2021-4-25-47
Abstract: We investigate the category of regular coverings of a given smooth principal bundle. A covering map of one principal bundle to another principal bundle is understood as a morphism in the category of principal bundles consisting of covering maps of their structural groups, total spaces and bases. The main results are: the construction of an invariant of a regular covering, which is a subsequence of the homotopy sequence of the base bundle; the existence theorem of a covering with a given invariant; criteria for morphisms and isomorphisms; a theorem on the automorphism group of a given covering. Bibliography: 21 titles.
Keywords: smooth manifold, principal bundle, covering, fundamental group.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2019-1931
Received: 05.05.2020
Revised: 05.05.2020
Accepted: 29.06.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 4, Pages 22–43
DOI: https://doi.org/10.3103/S1066369X21040034
Bibliographic databases:
Document Type: Article
UDC: 515.164
Language: Russian
Citation: T. A. Gonchar, E. I. Yakovlev, “Coverings in the category of principal bundles”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 4, 25–47; Russian Math. (Iz. VUZ), 65:4 (2021), 22–43
Citation in format AMSBIB
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\paper Coverings in the category of principal bundles
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2021
\issue 4
\pages 25--47
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\crossref{https://doi.org/10.26907/0021-3446-2021-4-25-47}
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\jour Russian Math. (Iz. VUZ)
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\vol 65
\issue 4
\pages 22--43
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:34
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