Geodesic
Almost principal bundles
Sbornik. Mathematics, Tome 190 (1999) no. 9, pp. 1377-1400 Cet article a éte moissonné depuis la source Math-Net.Ru

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The class $A$ of bundles with the following properties is investigated: each bundle in $A$ is the composition of a regular cover and a principal bundle (over the covering space) with Abelian structure group; the standard fibre $G$ of this decomposable bundle is a Lie group; the bundle has an atlas with multivalued transition functions taking values in the group $G$. The equivalence class of such an atlas will be called an almost principal bundle structure. The group of equivalence classes of almost principal bundles with a fixed base $B$ and a fixed structure group $G$ is computed, along with its subgroup of equivalence classes of principal $G$-bundles over $B$, and also the groups of equivalence classes of these bundles with respect to the morphisms of the category $C$ of decomposable bundles. A base and an invariant are found for an almost principal bundle that is not isomorphic to a principal bundle even in the category $C$. Applications are considered to the variational problem with fixed ends for multivalued functionals. 
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     author = {E. I. Yakovlev},
     title = {Almost principal bundles},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_9_a5/}
}
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E. I. Yakovlev. Almost principal bundles. Sbornik. Mathematics, Tome 190 (1999) no. 9, pp. 1377-1400. http://geodesic.mathdoc.fr/item/SM_1999_190_9_a5/

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