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- W2085907875 abstract "Given a principal G -bundle P over X , we define a particularly suitable equivalence relation between liftings of P with respect to a group morphism σ: M → G . Supposing that σ has a central kernel C , we obtain a free operation of H 1 ( X C ) (with coefficients in the sheaf of C -valued functions) on the set of lifting classes of P , which is natural under change of groups and base spaces. It is simply transitive, if in addition σ is an epimorphism; otherwise we classify its orbits by sections in the associated bundle P × G ( G /σ M ). For C= Z n we relate the lifting classes to similar classes of n -th roots of associated line bundles. In the differentiable case and for an epimorphism σ with discrete kernel, there is a natural lifting of partial principal connections in each of these lifting classes. Finally, we indicate some applications to geometric quantization." @default.
- W2085907875 created "2016-06-24" @default.
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- W2085907875 date "1980-12-01" @default.
- W2085907875 modified "2023-10-01" @default.
- W2085907875 title "Lifting classes of principal bundles" @default.
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- W2085907875 doi "https://doi.org/10.1016/0034-4877(80)90094-4" @default.
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