A formula for deviation from commutativity: the transfer and Steenrod squares

Kubelka, Richard P.

doi:10.1090/S0002-9939-1982-0647910-7

A formula for deviation from commutativity: the transfer and Steenrod squares
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by Richard P. Kubelka PDF

Proc. Amer. Math. Soc. 85 (1982), 119-124 Request permission

Abstract:

The ordinary cohomology transfer associated to the orbit space projection of a finite group action need not commute with stable cohomology operations. In particular, if an even group acts on a space, the resulting transfer $\tau$ will not generally commute with the Steenrod squares, ${\text {S}}{{\text {q}}^i}$. This paper contains a formula for the deviation from commutativity $({\text {S}}{{\text {q}}^i}\tau - \tau {\text {S}}{{\text {q}}^i})x$ in the case of an involution. The formula involves the restriction of $x$ to the cohomology of the fixed point set, as well as certain naturally occurring characteristic classes.

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The transfer and Steenrod squares

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