JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A NOTE ON THE UNSTABILITY CONDITIONS OF THE STEENROD SQUARES ON THE POLYNOMIAL ALGEBRA
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
A NOTE ON THE UNSTABILITY CONDITIONS OF THE STEENROD SQUARES ON THE POLYNOMIAL ALGEBRA
Janfada, Ali Sarbaz;
  PDF(new window)
 Abstract
We extend some results involved the action of the Steenrod operations on monomials and get some corollaries on the hit problem. Then, by multiplying some special matrices, we obtain an efficient tool to compute the action of these operations.
 Keywords
Steenrod squares;hit problem;
 Language
English
 Cited by
1.
On a conjecture on the symmetric hit problem, Rendiconti del Circolo Matematico di Palermo, 2011, 60, 3, 403  crossref(new windwow)
 References
1.
J Adem, The iteration of the Steenrod squares in algebraic topology, Proc. Nat. Acad. Sci. U. S. A. 38 (1952), 720.726 crossref(new window)

2.
H. Cartan, Une th$\acute{e}$orie axiomatique des carr$\acute{e}$s de Steenrod, C. R. Acad. Sci. Paris 230 (1950), 425.427

3.
L. E. Dickson, A fundamental system of invariants of the general modular linear group with a solution of the form problem, Trans. Amer. Math. Soc. 12 (1911), no. 1, 75.98 crossref(new window)

4.
J. Dieudonne, A History of Algebraic and Differential Topology, 1900.1960, Birkhauser Boston, Inc., Boston, MA, 1989

5.
J. R. Harper, Secondary Cohomology Operations, Graduate Studies in Mathematics, 49. American Mathematical Society, Providence, RI, 2002

6.
A. Hatcher, Algebraic Topology, Cambridge University Press, 2002

7.
A. S. Janfada, The hit problem for symmetric polynomials over the Steenrod algebra, Thesis, Manchester University, 2000

8.
A. S. Janfada, A criterion for a monomial in P(3) to be hit, Math. Proc. Camb. Phil. Soc. 145 (2008), 587.599 crossref(new window)

9.
A. S. Janfada and R. M. W. Wood, The hit problem for symmetric polynomials over the Steenrod algebra, Math. Proc. Cambridge Philos. Soc. 133 (2002), 295.303 crossref(new window)

10.
A. S. Janfada and R. M. W. Wood, Generating H*(BO(3), $\mathbb{F}_2$) as a module over the Steenrod algebra, Math. Proc. Cambridge Philos. Soc. 134 (2003), 239.258 crossref(new window)

11.
R. E. Mosher and M. C. Tangora, Cohomology operations and applications in homotopy theory, Harper & Row, Publishers, New York-London, 1968

12.
D. J. Pengelley and F. Williams, Global structure of the mod two symmetric algebra, H*(BO; $\mathbb{F}_2$), over the Steenrod algebra, Algebr. Geom. Topol. 3 (2003), 1119.1138 crossref(new window)

13.
D. J. Pengelley and F. Williams, Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology, Trans. Amer. Math. Soc. 352 (2000), no. 4, 1453.1492 crossref(new window)

14.
F. P. Peterson, Generators of H*($\mathbb{R}P{\vee}\mathbb{R}P$) as a module over the Steenrod algebra, Abstracts Amer. Math. Soc. 123 (1995), 627.637

15.
S. Priddy, On characterizing summands in the classifying space of a group. I, Amer. J. Math. 112 (1990), no. 5, 737.748 crossref(new window)

16.
J.-P. Serre, Cohomologie modulo 2 des complexes d'Eilenberg-MacLane, Comment. Math. Helv. 27 (1953), 198.232 crossref(new window)

17.
J. Silverman and W. M. Singer, On the action of Steenrod squares on polynomial algebras. II, J. Pure Appl. Algebra 98 (1995), no. 1, 95.103 crossref(new window)

18.
W. M. Singer, The transfer in homological algebra, Math. Z. 202 (1989), no. 4, 493.523 crossref(new window)

19.
W. M. Singer, Rings of symmetric functions as modules over the Steenrod algebra, Algebraic & Geometric Topology 8 (2008), 541.562 crossref(new window)

20.
L. Smith and R. M. Switzer, Realizability and nonrealizability of Dickson algebras as cohomology rings, Proc. Amer. Math. Soc. 89 (1983), no. 2, 303.313 crossref(new window)

21.
N. E. Steenrod, Products of cocycles and extensions of mappings, Ann. of Math. (2) 48 (1947), 290.320 crossref(new window)

22.
N. E. Steenrod and D. B. A. Epstein, Cohomology operations, Princeton University Press, 1962

23.
R. M. W. Wood, Modular representations of GL(n, $F_p$) and homotopy theory, Algebraic topology, $G{\ddot{o}}ttingen$ 1984, 188.203, Lecture Notes in Math., 1172, Springer, Berlin, 1985 crossref(new window)

24.
R. M. W. Wood, Problems in the Steenrod algebra, Bull. London Math. Soc. 30 (1998), no. 5, 449.517 crossref(new window)

25.
R. M. W. Wood, Steenrod squares of polynomials and the Peterson conjecture, Math. Proc. Cambridge Philos. Soc. 105 (1989), no. 2, 307.309 crossref(new window)