Geodesic
Existence theorem for coverings of Serre bundles
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2023), pp. 90-1.

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Coverings in the category of Serre bundles are investigated. A covering mapping of one such bundle onto another is understood as a morphism of the indicated category, consisting of covering mappings of total spaces and bases. Earlier, the author associated each such covering with a subsequence of the homotopy sequence of the base bundle. It was also shown that the conjugacy class of this subsequence is an invariant of the corresponding covering. The main result of this paper is the existence theorem of a covering with a given invariant. In addition, it is proved here that the local triviality of the base bundle implies a similar property for the covering bundle.
Keywords: Serre bundle, covering
Mots-clés : homotopy group. 
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E. I. Yakovlev. Existence theorem for coverings of Serre bundles. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2023), pp. 90-1. http://geodesic.mathdoc.fr/item/IVM_2023_3_a7/

[1] Gonchar T.A., Yakovlev E.I., “Nakrytiya v kategorii glavnykh rassloenii”, Izv. vuzov. Matem., 2021, no. 4, 25–47 | Zbl

[2] Gromol D., Klingenberg V., Meier V., Rimanova geometriya v tselom, Mir, M., 1971

[3] Yakovlev E.I., Gonchar T.A., “Geometriya i topologiya nekotorykh rassloennykh rimanovykh mnogoobrazii”, Izv. vuzov. Matem., 2018, no. 2, 77–95 | Zbl

[4] Skott P., Geometrii na trekhmernykh mnogoobraziyakh, Mir, M., 1986

[5] Lapteva A.V., Yakovlev E.I., “Index vector-function and minimal cycles”, Lobachevskii J. Math., 22 (2006), 35–46 | MR | Zbl

[6] Erickson J., Nayyeri A., “Minimum cuts and shortest non-separating cycles via homology covers”, Proc. 22nd Ann. ACM-SIAM Symp. Discrete Algorithms, 2011, 1166–1176 | DOI | MR | Zbl

[7] Zhukova N.I., “Attraktory i analog gipotezy Likhnerovicha dlya konformnykh sloenii”, Sib. matem. zhurn., 52:3 (2011), 555–574 | MR | Zbl

[8] Aranson S.Kh., Grines V.Z., “O predstavlenii minimalnykh mnozhestv potokov na dvumernykh mnogoobraziyakh geodezicheskimi liniyami”, Izv. AN SSSR. Ser. matem., 42:1 (1978), 104–129 | MR | Zbl

[9] Lerman L., Yakovlev E., “On interrelations between divergence-free and Hamiltonian dynamics”, J. Geom. and Phys., 135 (2019), 70–79 | DOI | MR | Zbl

[10] Yakovlev E.I., “Invarianty nakrytii rassloenii Serra”, Izv. vuzov. Matem., 2022, no. 3, 71–84

[11] Massi U., Stollings Dzh., Algebraicheskaya topologiya. Vvedenie, Mir, M., 1977

[12] Rokhlin V.A., Fuks D.B., Nachalnyi kurs topologii. Geometricheskie glavy, Nauka, M., 1977 | MR

[13] Grines V., Pochinka O., Levchenko Yu., Medvedev V., “The topological classification of structural stable 3-diffeomorphisms with two-dimensional basic sets”, Nonlinearity, 28 (2015), 4081–4102 | DOI | MR | Zbl

[14] Grines V.Z., Gurevich E.Ya., Kurenkov E.D., “O topologicheskoi klassifikatsii gradientno-podobnykh potokov s poverkhnostnoi dinamikoi na $3$-mnogoobraziyakh”, Matem. zametki, 107:1 (2020), 145–148 | DOI | MR | Zbl

[15] Grines V., Gurevich E., Pochinka O., “On the number of heteroclinic curves of diffeomorphisms with surface dynamics”, Regular and Chaotic Dynamics, 22:2 (2017), 122–135 | DOI | MR | Zbl

[16] Shubin D.D., “Topologiya nesuschikh mnogoobrazii nesingulyarnykh potokov s tremya neskruchennymi orbitami”, Izv. vuzov. Prikl. nelineinaya dinamika, 29:6 (2021), 863–868

[17] Epstein D.B.A., “Periodic flows on three-manifolds”, Ann. Math., 95:1 (1972), 66–82 | DOI | MR | Zbl