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 multiplicativ e units of the classical cohomology ring !!#»(*; Z/2) of a C^-complex X admits a transfer map N™: G(X)-+G(Y) defined 12=0 for finite coverings n : X—>Y, such that total Stiefel-Whitney class w: K0( )—>G( ) is a transfer commuting natural transformation. It is also shown that N™ 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).