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

Kozlowski, Andrzej

doi:10.1090/S0002-9939-1984-0740192-9

The Evens-Kahn formula for the total Stiefel-Whitney class
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by Andrzej Kozlowski PDF

Proc. Amer. Math. Soc. 91 (1984), 309-313 Request permission

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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