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The cohomology of finite H-spaces as U(M) algebras III

Published online by Cambridge University Press:  24 October 2008

Richard Kane
Richard Kane
Affiliation:
University of Western Ontario, London, Ontario, Canada
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Extract

In the previous papers in this series (see (5) and (6)) we used Brown-Peterson theory to obtain necessary conditions for the mod p cohomology of finite H-spaces to be U(M) algebras. In this paper we will use connective K-theory to strengthen the main results of (6). We should mention that we will be assuming a general knowledge of the previous two papers from this series. The definitions and notation from these papers will be used freely. (In particular, the reader is directed to § 2 of (5) for the definition of a U(M) algebra.)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 3 , November 1983 , pp. 461 - 471
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

(1)Clark, A.Homotopy commutativity and the Moore spectral sequence. Pacific J. Math. 15 (1965), 419–426.CrossRefGoogle Scholar
(2)Kane, R.The BP homology of H-spaces. Trans. Amer. Math. Soc. 241 (1978), 99–120.Google Scholar
(3)Kane, R.BP torsion in finite H-spaces. Trans. Amer. Math. Soc. 264 (1981), 473–497.Google Scholar
(4)Kane, R.Operations in connective K-theory. Memoirs Amer. Math. Soc. 254 (1981).Google Scholar
(5)Kane, R.The cohomology of finite H-spaces as U(M) Algebras: I. Math. Proc. Cambridge Philos. Soc. 89 (1981), 473–490.CrossRefGoogle Scholar
(6)Kane, R.The cohomology of finite H-spaces as U(M) algebras: II. Math. Proc. Cambridge Philon. Soc. 90 (1981), 113–125.CrossRefGoogle Scholar
(7)Kane, R.Finite H-spaces and the Thom map for connective K-Theory. Current trends in algebraic topology. Can. Math. Soc. Conference, vol. 2 (1982), pp. 389–415.Google Scholar
(8)Kane, R. The homology algebra of finite H-spaces. (To appear.)Google Scholar
(9)Lin, J.Torsion in H-spaces II. Annals of Math. 107 (1978), 41–88.CrossRefGoogle Scholar
(10)Milnor, J. and Moore, J. C.On the structure of Hopf algebras. Annals of Math. 81 (1965), 211–264.CrossRefGoogle Scholar