Some Formulas of the Action of Steenrod Powers on Cohomology Ring of K(Znp ; 2) Topological Space with coefficient Zp
Abstract
In this study we give some formulas for the action of the Steenrod Powers on certain monomials and some polynomials having these monomials as a factor in the polynomials algebra P(n) = Zp [x1; : : : ; xn], deg (xi) = 2, i = 1; : : : ; n and p is an odd prime. Also, we give some new family of hit polynomials.
References
- Steenrod, N.E., Products of cocycles and extensions of mappings, 48 (1947), 290-320.
- Steenrod, N.E., Cycles reduced powers of cohomology classes, Proc. Nat. Acad. Sci. U.S.A, 39 (1953), 217-223.
- Adams, J. F., On the non-existence of elements of Hopf invariant one, Ann. of Math., 72 (1960), 20-104.
- Steenrod, N.E., Whitehead, J.H.C., Vector elds on the n-sphere, Proc.Nat. Acad. Sci. U.S.A., 37 (1951), 58-63.
- Adams, J.F., On the structure and applications of the Steenrod algebra, Comm. Math. Helv., 32 (1958), 180-214.
- Adem, J., The iteration of Steenrod squares in algebraic topology, Proc. Nat. Acad. Sci. U.S.A, 38 (1952), 720-726.
- Cartan, H., Sur les groupes d'Eilenberg-Mac Lane. II, Proc. Nat. Acad. Sci. U.S.A, 40 (1954), 704-707.
- Cartan, H., Sur l'itration des oprations de Steenrod, Comment. Math. Helv., 29(1) (1955), 40-58.
- Serre, J.P., Cohomologie modulo 2 des complexes d'Eilenberg-Mac Lane, Comment. Math. Helv., 27 (1953), 198-231.
- Milnor, J., The Steenrod Algebra and its dual, Ann. Of Math., 67(2) (1958), 150-171.
- Steenrod, N.E., Epstein, D.B.A., Cohomology Operations, Princeton University Press, 1962.
- Wood, M.W.R., Problems in the Steenrod Algebra, Bull. London Math. Soc., 30 (1998), 499-517.
- Clark, A., Ewing, J., The realization of polynomial algebras as cohomology rings, Pasic J.Math., 50 (1974), 425-434.
- Janfada, A.S., On the action of the Steenrod squares on polynomial algebra, Miskolc Mathematical Notes, 8(2) (2007), 157-167.
- Hatcher, A., Algebraic Topology, Cambridge University Press, 2002.
- Wood, M.W.R., Walker, G., Polynomials and Steenrod Algebra, 2010.
Year 2013,
Volume: 4 , 15 - 26, 19.03.2014
Abstract
References
- Steenrod, N.E., Products of cocycles and extensions of mappings, 48 (1947), 290-320.
- Steenrod, N.E., Cycles reduced powers of cohomology classes, Proc. Nat. Acad. Sci. U.S.A, 39 (1953), 217-223.
- Adams, J. F., On the non-existence of elements of Hopf invariant one, Ann. of Math., 72 (1960), 20-104.
- Steenrod, N.E., Whitehead, J.H.C., Vector elds on the n-sphere, Proc.Nat. Acad. Sci. U.S.A., 37 (1951), 58-63.
- Adams, J.F., On the structure and applications of the Steenrod algebra, Comm. Math. Helv., 32 (1958), 180-214.
- Adem, J., The iteration of Steenrod squares in algebraic topology, Proc. Nat. Acad. Sci. U.S.A, 38 (1952), 720-726.
- Cartan, H., Sur les groupes d'Eilenberg-Mac Lane. II, Proc. Nat. Acad. Sci. U.S.A, 40 (1954), 704-707.
- Cartan, H., Sur l'itration des oprations de Steenrod, Comment. Math. Helv., 29(1) (1955), 40-58.
- Serre, J.P., Cohomologie modulo 2 des complexes d'Eilenberg-Mac Lane, Comment. Math. Helv., 27 (1953), 198-231.
- Milnor, J., The Steenrod Algebra and its dual, Ann. Of Math., 67(2) (1958), 150-171.
- Steenrod, N.E., Epstein, D.B.A., Cohomology Operations, Princeton University Press, 1962.
- Wood, M.W.R., Problems in the Steenrod Algebra, Bull. London Math. Soc., 30 (1998), 499-517.
- Clark, A., Ewing, J., The realization of polynomial algebras as cohomology rings, Pasic J.Math., 50 (1974), 425-434.
- Janfada, A.S., On the action of the Steenrod squares on polynomial algebra, Miskolc Mathematical Notes, 8(2) (2007), 157-167.
- Hatcher, A., Algebraic Topology, Cambridge University Press, 2002.
- Wood, M.W.R., Walker, G., Polynomials and Steenrod Algebra, 2010.
There are 16 citations in total.
Details
| Primary Language | English |
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| Authors | |
| Publication Date | March 19, 2014 |
| Published in Issue | Year 2013 Volume: 4 |