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Local formulae for Stiefel-Whitney classes

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Abstract

We construct an explicit Čech cocycle representing the k-th Stiefel-Whitney class of a vector bundle. This construction involves only the transition functions of the bundle. We also give local formulae for the secondary Stiefel-Whitney classes. These may be useful in determining whether the Stiefel-Whitney numbers of a flat bundle are zero.

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  1. Princeton University, 08544, Princeton, NJ, U.S.A.

    D. A. McLaughlin

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  1. D. A. McLaughlin
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McLaughlin, D.A. Local formulae for Stiefel-Whitney classes. Manuscripta Math 89, 1–13 (1996). https://doi.org/10.1007/BF02567501

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  • DOI: https://doi.org/10.1007/BF02567501

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