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Some Formulas of the Action of Steenrod Powers on Cohomology Ring of K(Znp ; 2) Topological Space with coefficient Zp

Year 2013, Volume: 4 , 15 - 26, 19.03.2014

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
Journal Section Mathematics
Authors

Bekir Tanay

Tarkan Öner This is me

Publication Date March 19, 2014
Published in Issue Year 2013 Volume: 4

Cite

APA Tanay, B., & Öner, T. (2014). Some Formulas of the Action of Steenrod Powers on Cohomology Ring of K(Znp ; 2) Topological Space with coefficient Zp. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy, 4, 15-26.
AMA Tanay B, Öner T. Some Formulas of the Action of Steenrod Powers on Cohomology Ring of K(Znp ; 2) Topological Space with coefficient Zp. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy. March 2014;4:15-26.
Chicago Tanay, Bekir, and Tarkan Öner. “Some Formulas of the Action of Steenrod Powers on Cohomology Ring of K(Znp ; 2) Topological Space With Coefficient Zp”. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy 4, March (March 2014): 15-26.
EndNote Tanay B, Öner T (March 1, 2014) Some Formulas of the Action of Steenrod Powers on Cohomology Ring of K(Znp ; 2) Topological Space with coefficient Zp. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy 4 15–26.
IEEE B. Tanay and T. Öner, “Some Formulas of the Action of Steenrod Powers on Cohomology Ring of K(Znp ; 2) Topological Space with coefficient Zp”, İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy, vol. 4, pp. 15–26, 2014.
ISNAD Tanay, Bekir - Öner, Tarkan. “Some Formulas of the Action of Steenrod Powers on Cohomology Ring of K(Znp ; 2) Topological Space With Coefficient Zp”. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy 4 (March 2014), 15-26.
JAMA Tanay B, Öner T. Some Formulas of the Action of Steenrod Powers on Cohomology Ring of K(Znp ; 2) Topological Space with coefficient Zp. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy. 2014;4:15–26.
MLA Tanay, Bekir and Tarkan Öner. “Some Formulas of the Action of Steenrod Powers on Cohomology Ring of K(Znp ; 2) Topological Space With Coefficient Zp”. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy, vol. 4, 2014, pp. 15-26.
Vancouver Tanay B, Öner T. Some Formulas of the Action of Steenrod Powers on Cohomology Ring of K(Znp ; 2) Topological Space with coefficient Zp. İstanbul University Science Faculty the Journal of Mathematics Physics and Astronomy. 2014;4:15-26.