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

Abstract

It is proved that G(X)-the group of multiplicative units of the classical cohomology ring Π\limits_i{≥}0H^l(X; Z/2) of a CW-complex X admits a transfer map N_π^w: 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 N_π^w 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”).