Multiplications on cohomology theories with coefficients

Martin, Alvin Frank

doi:10.1090/S0002-9947-1979-0536937-6

Multiplications on cohomology theories with coefficients
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Trans. Amer. Math. Soc. 253 (1979), 91-120 Request permission

Abstract:

Araki and Toda have considered the existence and classification of multiplications on generalized cohomology theories with coefficients in the category of finite CW-complexes. We consider the same matters for representable cohomology theories in a category of stable CW-spectra, such as that constructed by Adams. We obtain similar, and in certain instances stronger, results than Araki and Toda, with methods of proof that are often simpler and more straightforward.

References

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Stable homotopy and generalized homology

53

Shôrô Araki and Hirosi Toda, Multiplicative structures in $\textrm {mod}\,q$ cohomology theories. I, Osaka Math. J. 2 (1965), 71–115. MR 182967
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P. E. Conner and E. E. Floyd, The relation of cobordism to $K$-theories, Lecture Notes in Mathematics, No. 28, Springer-Verlag, Berlin-New York, 1966. MR 0216511, DOI 10.1007/BFb0071091
P. E. Conner and E. E. Floyd, Torsion in $\textrm {SU}$-bordism, Mem. Amer. Math. Soc. 60 (1966), 74. MR 189044

Notes on homotopy of Thorn spectra

80

29

Multiplications on

cohomology theories

C. R. F. Maunder, $\textrm {Mod}\,p$ cohomology theories and the Bockstein spectral sequence, Proc. Cambridge Philos. Soc. 63 (1967), 23-43; correction, ibid. 63 (1967), 935. MR 0211395, DOI 10.1017/s0305004100041931