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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The Evens-Kahn formula for the total Stiefel-Whitney class


Author: Andrzej Kozlowski
Journal: Proc. Amer. Math. Soc. 91 (1984), 309-313
MSC: Primary 55N15; Secondary 20J06, 55P47, 55R40, 57R20
MathSciNet review: 740192
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Abstract: Let $ G\left( X \right)$ denote the (augmented) multiplicative group of classical cohomology ring of a space $ X$, with coefficients in $ Z/2$. The (augmented) total Stiefel-Whitney class is a natural homomorphism $ w:KO\left( X \right) \to G\left( X \right)$. We show that the functor $ G\left( {} \right)$ possesses a 'transfer homomorphism' for double coverings such that $ w$ commutes with the transfer. This is related to a question of G. Segal. As a special case, we obtain a formula for the total Stiefel-Whitney class of a representation of a finite group induced from a (real) representation of a subgroup of index 2, which is analogous to the one obtained by Evens and Kahn for the total Chern class.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740192-9
PII: S 0002-9939(1984)0740192-9
Keywords: Generalized cohomology theory, transfer homomorphism, total Stiefel-Whitney class
Article copyright: © Copyright 1984 American Mathematical Society