Geodesic
Smooth almost $\Delta$-fiber bundles over simplicial complexes
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2010), pp. 3-21

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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 
@article{IVM_2010_11_a0,
     author = {V. Y. Zinchenko and E. I. Yakovlev},
     title = {Smooth almost $\Delta$-fiber bundles over simplicial complexes},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--21},
     publisher = {mathdoc},
     number = {11},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_11_a0/}
}
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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/