Cohomology morphisms from $H^ *(B\textrm {U};\textbf {Z}/p)$ to $H^ *(B\textbf {Z}/p;\textbf {Z}/p)$
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- by Terrence Paul Bisson PDF
- Proc. Amer. Math. Soc. 101 (1987), 363-370 Request permission
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
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T. P. Bisson, Divided sequences and bialgebras of homology operations, Ph.D. Thesis, Duke Univ., Durham, N. C, 1977.
- S. R. Bullett and I. G. Macdonald, On the Adem relations, Topology 21 (1982), no.Β 3, 329β332. MR 649764, DOI 10.1016/0040-9383(82)90015-5
- Gunnar Carlsson, G. B. Segalβs Burnside ring conjecture for $(\textbf {Z}/2)^{k}$, Topology 22 (1983), no.Β 1, 83β103. MR 682060, DOI 10.1016/0040-9383(83)90046-0
- Murray Gerstenhaber and Samuel D. Schack, Relative Hochschild cohomology, rigid algebras, and the Bockstein, J. Pure Appl. Algebra 43 (1986), no.Β 1, 53β74. MR 862872, DOI 10.1016/0022-4049(86)90004-6 J. Lannes, Sur la cohomologie modulo $p$ des $p$-groupes abelians elementaires, preprint.
- Haynes Miller, The Sullivan conjecture on maps from classifying spaces, Ann. of Math. (2) 120 (1984), no.Β 1, 39β87. MR 750716, DOI 10.2307/2007071
- D. W. Anderson and Luke Hodgkin, The $K$-theory of Eilenberg-MacLane complexes, Topology 7 (1968), 317β329. MR 231369, DOI 10.1016/0040-9383(68)90009-8
- Andrzej Jankowski, Splitting of $K$-theory and $g_\ast$ characteristic numbers, Studies in algebraic topology, Adv. in Math. Suppl. Stud., vol. 5, Academic Press, New York-London, 1979, pp.Β 189β212. MR 527250
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 363-370
- MSC: Primary 55S10; Secondary 55R35, 55R40
- DOI: https://doi.org/10.1090/S0002-9939-1987-0902557-4
- MathSciNet review: 902557