Geodesic
Coverings in the category of principal bundles
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2021), pp. 25-47

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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. 
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     author = {T. A. Gonchar and E. I. Yakovlev},
     title = {Coverings in the category of principal bundles},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {25--47},
     publisher = {mathdoc},
     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_4_a2/}
}
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T. A. Gonchar; E. I. Yakovlev. Coverings in the category of principal bundles. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2021), pp. 25-47. http://geodesic.mathdoc.fr/item/IVM_2021_4_a2/