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- W2059131346 abstract "Let be a principal -bundle over a smooth compact manifold given by a finite atlas with transition functions . A method is described for constructing the cocycles corresponding to the Chern classes of the bundle in the Cech complex with coefficients in the sheaf of de Rham forms on the manifold associated with the atlas . It is proved that for every rational characteristic class of the bundle there exists a cocycle in the aforementioned complex depending only on the gluing functions and corresponding to the class under the canonical identification of the cohomologies of the complex and the de Rham cohomologies of the manifold (a simple algorithm is given that enables one to calculate this cocycle explicitly). One of the key ideas leading to these results is the idea of using the notion of a twisting cochain for constructing the cocycles.Bibliography: 14 titles." @default.
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- W2059131346 date "2008-10-31" @default.
- W2059131346 modified "2023-09-23" @default.
- W2059131346 title "Local formulae for characteristic classes of a principal GL<sub><i>n</i></sub>-bundle" @default.
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- W2059131346 doi "https://doi.org/10.1070/sm2008v199n10abeh003972" @default.
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