Geodesic
Invariants of coverings of Serre bundles
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2022), pp. 71-84.

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The category of coverings of a given Serre bundle is investigated. By a covering mapping of one such bundle onto another we mean a morphism in the category of bundles consisting of covering mappings of total spaces and bases. An invariant of a covering from the indicated category is constructed, which is the conjugacy class of some subsequence of the homotopy sequence of the base bundle. Criteria for the existence of morphisms and isomorphisms for given coverings are obtained.
Keywords: Serre bundle, covering
Mots-clés : homotopy group. 
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E. I. Yakovlev. Invariants of coverings of Serre bundles. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2022), pp. 71-84. http://geodesic.mathdoc.fr/item/IVM_2022_3_a7/

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

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

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

[4] 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

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

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

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

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

[9] Yakovlev E. I., “O suschestvovanii reshenii dvukhtochechnykh kraevykh zadach dlya giroskopicheskikh sistem relyativistskogo tipa”, Algebra i analiz, 9:2 (1997), 256–271

[10] Ershov Yu. V., Yakovlev E. I., “Obobschennye funktsii rasstoyaniya rimanovykh mnogoobrazii i dvizheniya giroskopicheskikh sistem”, Sib. matem. zhurn., 49:1 (2008), 87–100 | MR | Zbl

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

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

[13] Spener E., Algebraicheskaya topologiya, Mir, M., 1971

[14] Kurosh A. G., Teoriya grupp, Nauka, M., 1967 | MR

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