Steenrod operation
From Encyclopedia of Mathematics
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 $p$.
References
[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: http://www.encyclopediaofmath.org/index.php?title=Steenrod_operation&oldid=24818
Steenrod operation. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Steenrod_operation&oldid=24818
This article was adapted from an original article by Yu.B. Rudyak (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article