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A note on the unstability conditions of the Steenrod squares on the polynomial algebra

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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.

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.

참고문헌 (25)

  1. J Adem, "The iteration of the Steenrod squares in algebraic topology", Proc. Nat. Acad. Sci. U. S. A., 38, pp.720~726 (1952)
  2. H. Cartan, "Une the´orie axiomatique des carr´es de Steenrod", C. R. Acad. Sci. Paris, 230, pp.425~427 (1950)
  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(1), pp.75~98 (1911)
  4. J. Dieudonn´e, "A History of Algebraic and Differential Topology", pp.1900~1960 (1989), Birkhauser Boston, Inc.
  5. J. R. Harper, "Secondary Cohomology Operations, Graduate Studies in Mathematics", American Mathematical Society, 49 (2002)
  6. A. Hatcher, "Algebraic Topology" (2002), Cambridge University Press
  7. A. S. Janfada, "The hit problem for symmetric polynomials over the Steenrod algebra" (2000), Thesis, Manchester University
  8. A. S. Janfada, "A criterion for a monomial in P(3) to be hit", Math. Proc. Camb. Phil. Soc., 145, pp.587~599 (2008)
  9. A. S. Janfada, "The hit problem for symmetric polynomials over the Steenrod algebra", Math. Proc. Cambridge Philos. Soc., 133, pp.295~303 (2002)
  10. A. S. Janfada, "Generating H¤(BO(3), F2) as a module over the Steenrod algebra", Math. Proc. Cambridge Philos. Soc., 134, pp.239~258 (2003)
  11. R. E. Mosher, "Cohomology operations and applications in homotopy theory" (1968), Harper & Row, Publishers
  12. D. J. Pengelley, "Global structure of the mod two symmetric algebra, H¤(BO; F2), over the Steenrod algebra", Algebr. Geom. Topol., 3, pp.1119~1138 (2003)
  13. D. J. Pengelley, "Sheared algebra maps and operation bialgebras for mod 2 homology and cohomology", Trans. Amer. Math. Soc., 352(4), pp.1453~1492 (2000)
  14. F. P. Peterson, "Generators of H¤(RP _ RP) as a module over the Steenrod algebra", Abstracts Amer. Math. Soc., 123, pp.627~637 (1995)
  15. S. Priddy, "On characterizing summands in the classifying space of a group", I, Amer. J. Math., 112(5), pp.737~748 (1990)
  16. J.-P. Serre, "Cohomologie modulo 2 des complexes d’Eilenberg-MacLane", Comment. Math. Helv., 27, pp.198~232 (1953)
  17. J. Silverman, "On the action of Steenrod squares on polynomial algebras", II, J. Pure Appl. Algebra, 98(1), pp.95~103 (1995)
  18. W. M. Singer, "The transfer in homological algebra", Math. Z., 202(4), pp.493~523 (1989)
  19. W. M. Singer, "Rings of symmetric functions as modules over the Steenrod algebra", Algebraic & Geometric Topology, 8, pp.541~562 (2008)
  20. L. Smith, "Realizability and nonrealizability of Dickson algebras as cohomology rings", Proc. Amer. Math. Soc., 89(2), pp.303~313 (1983)
  21. N. E. Steenrod, "Products of cocycles and extensions of mappings", Ann. of Math., 48, pp.290~320 (1947)
  22. N. E. Steenrod, "Cohomology operations" (1962), Princeton University Press
  23. R. M. W. Wood, "Modular representations of GL(n, Fp) and homotopy theory, Algebraic topology, G¨ottingen", Lecture Notes in Math., 1172, pp.188~203 (1985), Springer
  24. R. M. W. Wood, "Problems in the Steenrod algebra", Bull. London Math. Soc., 30(5), pp.449~517 (1998)
  25. R. M. W. Wood, "Steenrod squares of polynomials and the Peterson conjecture", Math. Proc. Cambridge Philos. Soc., 105(2), pp.307~309 (1989)

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