K-theory and the anti-automorphism of the Steenrod algebra

Crabb, M.; Crossley, M.; Hubbuck, J.

doi:10.1090/S0002-9939-96-03388-6

K-theory and the anti-automorphism of the Steenrod algebra
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by M. C. Crabb, M. D. Crossley and J. R. Hubbuck PDF

Proc. Amer. Math. Soc. 124 (1996), 2275-2281 Request permission

Abstract:

We give simple proofs of some relations in the Steenrod algebra involving the powers $\mathcal {P}^i$ and their duals $\chi \mathcal {P}^i$ and show how these relations arise from $K$-theory.

References

J. F. Adams, On Chern characters and the structure of the unitary group, Proc. Cambridge Philos. Soc. 57 (1961), 189–199. MR 121795, DOI 10.1017/s0305004100035052
M. F. Atiyah and F. Hirzebruch, Cohomologie-Operationen und charakteristische Klassen, Math. Z. 77 (1961), 149–187 (German). MR 156361, DOI 10.1007/BF01180171
M. G. Barratt and H. R. Miller, On the Anti-automorphism of the Steenrod Algebra, Contemp. Math. 12, (1981), 47–52.
S. R. Bullett and I. G. Macdonald, On the Adem relations, Topology 21 (1982), no. 3, 329–332. MR 649764, DOI 10.1016/0040-9383(82)90015-5
M. C. Crabb, S. Jäschke and K. Knapp, The Im(J)-theory Chern character, manuscript, 1992.
M. D. Crossley, Results concerning the Steenrod Algebra, Thesis, University of Aberdeen, 1995.
M. D. Crossley and J. R. Hubbuck, Not The Adem Relations, Bol. Soc. Mat. Mexicana 37, (1992), 99–105.
J. R. Hubbuck, Primitivity in torsion free cohomology Hopf algebras, Comment. Math. Helv. 46 (1971), 13–43. MR 288762, DOI 10.1007/BF02566825
N. E. Steenrod, Cohomology operations, Annals of Mathematics Studies, No. 50, Princeton University Press, Princeton, N.J., 1962. Lectures by N. E. Steenrod written and revised by D. B. A. Epstein. MR 0145525
Philip D. Straffin Jr., Identities for conjugation in the Steenrod algebra, Proc. Amer. Math. Soc. 49 (1975), 253–255. MR 380796, DOI 10.1090/S0002-9939-1975-0380796-3