Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Cohomology morphisms from $ H\sp *(B{\rm U};{\bf Z}/p)$ to $ H\sp *(B{\bf Z}/p;{\bf Z}/p)$

Author: Terrence Paul Bisson
Journal: Proc. Amer. Math. Soc. 101 (1987), 363-370
MSC: Primary 55S10; Secondary 55R35, 55R40
MathSciNet review: 902557
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we use Hopf algebra and generating function methods to determine the group of all cohomology morphisms from $ {H^ * }\left( {BU;Z/p} \right)$ to $ {H^ * }\left( {BZ/p;Z/p} \right)$ that preserve the Steenrod operations, where $ p$ is an odd prime. The group $ \left[ {BZ/p,BU} \right]$ of homotopy classes of maps from $ BZ/p$ to BU, which can be calculated directly, is seen to be naturally isomorphic to the group of cohomology morphisms. For $ BZ/2$ and BO with coefficients in $ Z/2$ there are precisely similar results.

References [Enhancements On Off] (What's this?)

  • [1] T. P. Bisson, Divided sequences and bialgebras of homology operations, Ph.D. Thesis, Duke Univ., Durham, N. C, 1977.
  • [2] S. R. Bullett and I. G. MacDonald, On the Adem relations, Topology 21 (1982), 329-332. MR 649764 (83h:55035)
  • [3] G. Carlsson, G. B. Segal's Burnside ring conjecture for $ {\left( {Z/2} \right)^K}$, Topology 22 (1983), 83-103. MR 682060 (84a:55007)
  • [4] M. Gerstenhaber and S. D. Schack, Relative Hochschild cohomology, rigid algebras, and the Bockstein, J. Pure Appl. Algebra (to appear). MR 862872 (88a:16045)
  • [5] J. Lannes, Sur la cohomologie modulo $ p$ des $ p$-groupes abelians elementaires, preprint.
  • [6] H. R. Miller, The Sullivan conjecture on maps from classifying spaces, Ann. of Math. 120 (1984), 39-87; 121 (1985), 605-609. MR 750716 (85i:55012)
  • [7] D. W. Anderson and L. Hodgkin, The $ K$-theory of Eilenberg-Mac Lane complexes, Topology 7 (1968), 317-329. MR 0231369 (37:6924)
  • [8] A. Jankowski, Splitting of $ K$-theory and $ {g^ * }$ characteristic numbers, Studies in Algebraic Topology (Adv. in Math. Suppl. Stud., Vol. 5), Academic Press, 1979. MR 527250 (80e:55008)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55S10, 55R35, 55R40

Retrieve articles in all journals with MSC: 55S10, 55R35, 55R40

Additional Information

Keywords: Classifying spaces, Steenrod operations, generating functions, $ p$-adic numbers
Article copyright: © Copyright 1987 American Mathematical Society

American Mathematical Society