Difference between revisions of "Steenrod operation"
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| − | The general name for the stable cohomology operations (cf. [[Cohomology operation|Cohomology operation]]) created by N.E. Steenrod for every prime number | + | {{TEX|done}} |
| + | The general name for the stable cohomology operations (cf. [[Cohomology operation|Cohomology operation]]) created by N.E. Steenrod for every prime number $p$. The first example is contained in [[#References|[1]]]. For $p=2$ this is the [[Steenrod square|Steenrod square]] $Sq^i$, for $p>2$ the [[Steenrod reduced power|Steenrod reduced power]] $\mathcal{P}^i$. The operations $Sq^i$ multiplicatively generate the [[Steenrod algebra|Steenrod algebra]] modulo 2, while the operations $\mathcal{P}^i$ together with the Bockstein homomorphism generate the Steenrod algebra modulo $p$. | ||
====References==== | ====References==== | ||
Revision as of 21:04, 19 April 2012
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 [1]. 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
| [1] | N.E. Steenrod, "Products of cocycles and extensions of mappings" Ann. of Math. , 48 (1947) pp. 290–320 |
| [2] | N.E. Steenrod, D.B.A. Epstein, "Cohomology operations" , Princeton Univ. Press (1962) |
| [3] | M.K. Tangora, "Cohomology operations and applications in homotopy theory" , Harper & Row (1968) |
Comments
References
| [a1] | R.M. Switzer, "Algebraic topology - homotopy and homology" , Springer (1975) pp. Chapt. 18 |
| [a2] | J.F. Adams, "Stable homotopy and generalized homology" , Univ. Chicago Press (1974) pp. Part III, Chapt. 12 |
How to Cite This Entry:
Steenrod operation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Steenrod_operation&oldid=18169
Steenrod operation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Steenrod_operation&oldid=18169
This article was adapted from an original article by Yu.B. Rudyak (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article