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1999 | 160 | 1 | 81-93
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Multiplicative operations in the Steenrod algebra for Brown–Peterson cohomology

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A family of multiplicative operations in the BP Steenrod algebra is defined which is related to the total Steenrod power operation from the mod p Steenrod algebra. The main result of the paper links the BP versions of the total Steenrod power with the formal group approach to multiplicative BP operations by identifying the p-typical curves (power series) which correspond to these operations. Some relations are derived from this identification, and a short proof of the Hopf invariant one theorem is given as a sample computation.
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Twórcy
  • Department of Mathematics and Statistics, Western Michigan University, Kalamazoo, Michigan 49008-5152, U.S.A., slack@math-stat.wmich.edu
Bibliografia
  • [1] J. F. Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. 72 (1960), 20-104.
  • [2] S. Araki, Multiplicative operations in BP cohomology, Osaka J. Math. 12 (1975), 343-356.
  • [3] J. M. Boardman, The eightfold way to BP operations, Canad. Math. Soc. Proc. 2 (1982), 187-226.
  • [4] J. R. Hubbuck, Generalized cohomology operations and H-spaces of low rank, Trans. Amer. Math. Soc. 141 (1969), 335-360.
  • [5] R. Kane, Rational BP operations and the Chern character, Math. Proc. Cambridge Philos. Soc. 84 (1978), 65-72.
  • [6] R. Kane, Brown-Peterson operations and Steenrod modules, Quart. J. Math. Oxford 30 (1979), 455-467.
  • [7] P. S. Landweber, Homological properties of comodules over $MU_*MU$ and BP$_*$BP, Amer. J. Math. 98 (1976), 591-610.
  • [8] A. L. Liulevicius, The factorization of cyclic reduced powers by secondary cohomology operations, Mem. Amer. Math. Soc. 42 (1962).
  • [9] J. W. Milnor, The Steenrod algebra and its dual, Ann. of Math. 67 (1958), 150-171.
  • [10] D. C. Ravenel, Complex Cobordism and Stable Homotopy Groups of Spheres, Academic Press, 1986.
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bwmeta1.element.bwnjournal-article-fmv160i1p81bwm
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