Hostname: page-component-848d4c4894-4hhp2 Total loading time: 0 Render date: 2024-05-01T05:20:05.339Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Pontrjagin rings, I

Published online by Cambridge University Press:  14 November 2011

J. R. Hubbuck
J. R. Hubbuck
Affiliation:
Department of Mathematics, University of Aberdeen, Edward Wright Building, Aberdeen AB9 2TY
Get access Rights & Permissions [Opens in a new window]

Synopsis

The H-spaces considered have no homology p-torsion and are rationally equivalent as H-spaces to products of even dimensional Eilenberg–Maclane spaces. We obtain conditions which ensure that if the cohomology with coefficients in the ring of integers localized at the prime p is a polynomial algebra, then the Pontrjagin ring with these same coefficients is polynomial. A topological consequence is that BSUP has just one homotopy associative, homotopy commutative H-structure.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 3-4 , 1981 , pp. 237 - 256
Copyright
Copyright © Royal Society of Edinburgh 1981

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

1Adams, J. F.. On Chern characters and the structure of the unitary group. Proc. Cambridge Philos. Soc. 57 (1961), 189–199.CrossRefGoogle Scholar
2Adams, J. F.. Generalized cohomology, lecture 4. Category theory, homology theory and their applications III. Lecture Notes in Mathematics 99, pp. 77–113 (Berlin: Springer, 1969).Google Scholar
3Adams, J. F.. Primitive elements in the K-theory of BSU. Quart. J. Math. Oxford 27 (1976), 253–262.CrossRefGoogle Scholar
4Hubbuck, J. R.. Finitely generated cohomology Hopf algebras. Topology 9 (1970), 205–210.CrossRefGoogle Scholar
5Hubbuck, J. R.. Primitivity in torsion free cohomology Hopf algebras. Comment. Math. Helv. 46 (1971), 13–43.CrossRefGoogle Scholar
6Hubbuck, J. R.. A Hopf algebra decomposition theorem. Bull. London Math. Soc. 13 (1981), 125–128.CrossRefGoogle Scholar
7.Husemoller, D.. The structure of the Hopf algebra H*(BU) over a Z (p)-algebra. Amer. J. Math. 93 (1971), 329–349.CrossRefGoogle Scholar
8Lin, J.. Torsion in H-spaces I. Ann. of Math. 103 (1976), 457–487.CrossRefGoogle Scholar
9Lin, J.. Torsion in H-spaces II. Ann. of Math. 107 (1978), 41–88.CrossRefGoogle Scholar
10Lin, J.. H-spaces without simple torsion. J. Pure Appl. Algebra 11 (1977), 61–66.CrossRefGoogle Scholar
11Milnor, J..and Moore, J.. On the structure of Hopf algebras. Ann. of Math. 81 (1965), 211–264.CrossRefGoogle Scholar
12Zabrodsky, A.. Hopf spaces. Notas de Matmatica 22 (Amsterdam: North-Holland, 1976).Google Scholar