Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T13:11:21.306Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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