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This article is cited in 3 scientific papers (total in 3 papers)
Almost principal bundles
E. I. Yakovlev N. I. Lobachevski State University of Nizhni Novgorod
Abstract:
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.
Received: 22.07.1998 and 08.06.1999
Citation:
E. I. Yakovlev, “Almost principal bundles”, Mat. Sb., 190:9 (1999), 151–176; Sb. Math., 190:9 (1999), 1377–1400
Linking options:
https://www.mathnet.ru/eng/sm429https://doi.org/10.1070/sm1999v190n09ABEH000429 https://www.mathnet.ru/eng/sm/v190/i9/p151
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Abstract page: | 347 | Russian version PDF: | 180 | English version PDF: | 6 | References: | 50 | First page: | 2 |
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