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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 11, Pages 3–21 (Mi ivm7146)  
Smooth almost $\Delta$-fiber bundles over simplicial complexes

V. Y. Zinchenko, E. I. Yakovlev

Chair of Geometry and Higher Algebra, Nizhni Novgorod State University, Nizhni Novgorod, Russia
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Abstract: 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, invariant connection, almost $\Delta$-bundles.
Received: 31.03.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 11, Pages 1–17
DOI: https://doi.org/10.3103/S1066369X10110010
Bibliographic databases:
Document Type: Article
UDC: 515.164
Language: Russian
Citation: V. Y. Zinchenko, E. I. Yakovlev, “Smooth almost $\Delta$-fiber bundles over simplicial complexes”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 11, 3–21; Russian Math. (Iz. VUZ), 54:11 (2010), 1–17
Citation in format AMSBIB
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\by V.~Y.~Zinchenko, E.~I.~Yakovlev
\paper Smooth almost $\Delta$-fiber bundles over simplicial complexes
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 11
\pages 3--21
\mathnet{http://mi.mathnet.ru/ivm7146}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2814560}
\elib{https://elibrary.ru/item.asp?id=14865173}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 11
\pages 1--17
\crossref{https://doi.org/10.3103/S1066369X10110010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649605406}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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