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 . The first example is contained in [1]. For
this is the Steenrod square
, for
the Steenrod reduced power
. The operations
multiplicatively generate the Steenrod algebra modulo 2, while the operations
together with the Bockstein homomorphism generate the Steenrod algebra modulo
.
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=24815
Steenrod operation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Steenrod_operation&oldid=24815
This article was adapted from an original article by Yu.B. Rudyak (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article