Geodesic
Smooth almost $\Delta$-fiber bundles over simplicial complexes
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2010), pp. 3-21 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we construct and study a category of principal fiber bundles with the following properties: 1) the base is a simplicial complex and the structure group is a $k$-dimensional torus, 2) maps of any atlas are smooth on every simplex of the base, and 3) the finite group $\Delta$ acts on the base and this action has a multi-valued lifting to the total space. We study invariant connections and built integer-valued realizable characteristic classes.
Keywords: simplicial complex, simplicial group action, Thom–Whitney forms, principal fiber bundle, multi-valued action, almost $\Delta$-bundles.
Mots-clés : invariant connection 
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V. Y. Zinchenko; E. I. Yakovlev. Smooth almost $\Delta$-fiber bundles over simplicial complexes. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2010), pp. 3-21. http://geodesic.mathdoc.fr/item/IVM_2010_11_a0/

[1] Novikov S. P., “Gamiltonov formalizm i mnogoznachnyi analog teorii Morsa”, UMN, 37:5 (1982), 3–49 | MR | Zbl

[2] Yakovlev E. I., “Rassloeniya i geometricheskie struktury, assotsiirovannye s giroskopicheskimi sistemami”, Sovremennaya matematika. Fundamentalnye napravleniya, 22, 2007, 100–126 | MR

[3] Ryzhkova A. B., Yakovlev E. I., “Rassloeniya s gruppami mnogoznachnykh avtomorfizmov”, Matem. zametki, 77:4 (2005), 600–616 | MR | Zbl

[4] Lemann D., “Gomotopicheskaya teoriya differentsialnykh form”, Matematika. Novoe v zarubezhnoi nauke, Mir, M., 1981, 7–85 | MR

[5] Uitnei Kh., Geometricheskaya teoriya integrirovaniya, In. lit., M., 1969

[6] Uorner F., Osnovy teorii gladkikh mnogoobrazii i grupp Li, Mir, M., 1987 | MR

[7] Suon R. Dzh., “Teoriya Toma differentsialnykh form na simplitsialnykh mnozhestvakh”, Matematika. Novoe v zarubezhnoi nauke, Mir, M., 1981, 172–176

[8] Mankrs Dzh., “Elementarnaya differentsialnaya topologiya”, Dopolnenie v kn.: Milnor Dzh., Stashef Dzh., Kharakteristicheskie klassy, Mir, M., 1979 | MR

[9] Postnikov M. M., Vvedenie v teoriyu Morsa, Nauka, M., 1971 | MR

[10] Bredon G., Vvedenie v teoriyu kompaktnykh grupp preobrazovanii, Nauka, M., 1980 | MR | Zbl

[11] Ryzhkova A. B., Yakovlev E. I., “Glavnye rassloeniya, dopuskayuschie pochti invariantnye struktury”, Izv. vuzov. Matematika, 2007, no. 8, 48–59 | MR | Zbl

[12] Moerdijk I., Pronk D. A., “Simplicial cohomology of orbifolds”, Indag. Math. New Ser., 10:2 (1999), 269–293 | DOI | MR | Zbl