BibTex RIS Kaynak Göster

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

Yıl 2013, Cilt: 4 , 15 - 26, 19.03.2014

Öz

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.

Kaynakça

  • 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.
Yıl 2013, Cilt: 4 , 15 - 26, 19.03.2014

Öz

Kaynakça

  • 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.
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Matematik
Yazarlar

Bekir Tanay

Tarkan Öner Bu kişi benim

Yayımlanma Tarihi 19 Mart 2014
Yayımlandığı Sayı Yıl 2013 Cilt: 4

Kaynak Göster

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. Mart 2014;4:15-26.
Chicago Tanay, Bekir, ve 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, Mart (Mart 2014): 15-26.
EndNote Tanay B, Öner T (01 Mart 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 ve 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, c. 4, ss. 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 (Mart 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 ve 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, c. 4, 2014, ss. 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.