Steenrod operation

From Encyclopedia of Mathematics
Jump to: navigation, search

The general name for the stable cohomology operations (cf. Cohomology operation) created by N.E. Steenrod for every prime number $p$. The first example is contained in [St]. For $p=2$ this is the Steenrod square $Sq^i$, for $p>2$ the Steenrod reduced power $\mathcal{P}^i$. The operations $Sq^i$ multiplicatively generate the Steenrod algebra modulo 2, while the operations $\mathcal{P}^i$ together with the Bockstein homomorphism generate the Steenrod algebra modulo $p$.


[Ad] J.F. Adams, "Stable homotopy and generalized homology", Univ. Chicago Press (1974) pp. Part III, Chapt. 12
[St] N.E. Steenrod, "Products of cocycles and extensions of mappings" Ann. of Math., 48 (1947) pp. 290–320
[StEp] N.E. Steenrod, D.B.A. Epstein, "Cohomology operations", Princeton Univ. Press (1962)
[Sw] R.M. Switzer, "Algebraic topology - homotopy and homology", Springer (1975) pp. Chapt. 18
[Ta] M.K. Tangora, "Cohomology operations and applications in homotopy theory", Harper & Row (1968)
How to Cite This Entry:
Steenrod operation. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by Yu.B. Rudyak (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article