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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Richard P. Kubelka
Journal: Proc. Amer. Math. Soc. 85 (1982), 119-124
MSC: Primary 55R99; Secondary 55S10, 57S17
MathSciNet review: 647910
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0647910-7
PII: S 0002-9939(1982)0647910-7
Keywords: Transfer, Steenrod squares, involution, fixed point set
Article copyright: © Copyright 1982 American Mathematical Society