Transfers in the Group of Multiplicative Units of the Classical Cohomology Ring and Stiefel-Whitney Classes

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It is proved that G(X)-the group of multiplicative units of the classical cohomology ring Π\limitsi{≥}0Hl(X; Z/2) of a CW-complex X admits a transfer map Nπw: G(X)→G(Y) defined for finite coverings π: X→Y, such that total Stiefel-Whitney class w: KO( )→G( ) is a transfer commuting natural transformation. It is also shown that Nπw possesses all the properties of transfers in generalized cohomology theories and for double coverings can be expressed in terms of the Evens transfer (“Evens norm”).

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