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.
@article{SM_1999_190_9_a5,
author = {E. I. Yakovlev},
title = {Almost principal bundles},
journal = {Sbornik. Mathematics},
pages = {1377--1400},
year = {1999},
volume = {190},
number = {9},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1999_190_9_a5/}
}
TY - JOUR
AU - E. I. Yakovlev
TI - Almost principal bundles
JO - Sbornik. Mathematics
PY - 1999
SP - 1377
EP - 1400
VL - 190
IS - 9
UR - http://geodesic.mathdoc.fr/item/SM_1999_190_9_a5/
LA - en
ID - SM_1999_190_9_a5
ER -
%0 Journal Article
%A E. I. Yakovlev
%T Almost principal bundles
%J Sbornik. Mathematics
%D 1999
%P 1377-1400
%V 190
%N 9
%U http://geodesic.mathdoc.fr/item/SM_1999_190_9_a5/
%G en
%F SM_1999_190_9_a5
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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