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A $ p$-local splitting of $ B{\rm U}(n)$


Author: Kenshi Ishiguro
Journal: Proc. Amer. Math. Soc. 95 (1985), 307-311
MSC: Primary 55R35; Secondary 55R40
DOI: https://doi.org/10.1090/S0002-9939-1985-0801344-3
MathSciNet review: 801344
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Abstract: Let $ p$ be a prime and let $ n > 1$. A necessary and sufficient condition that the classifying space $ BU(n)$ is $ p$-equivalent to the product of nontrivial spaces is that $ p$ does not divide $ n$.


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  • [1] J. F. Adams and Z. Mahmud, Maps between classifying spaces, Invent. Math. 35 (1976), 1-41. MR 0423352 (54:11331)
  • [2] J. F. Adams and C. W. Wilkerson, Finite $ H$-spaces and algebras over the Steenrod algebra, Ann. of Math. 111 (1980), 95-143. MR 558398 (81h:55006)
  • [3] A. Borel, Sur la cohomologie des espaces fibres principaux et des espaces homogenes de groupes de Lie compacts, Ann. of Math. 57 (1953), 115-207. MR 0051508 (14:490e)
  • [4] A. Clark and J. Ewing, The realization of polynomial algebras as cohomology rings, Pacific J. Math. 50 (1974), 425-434. MR 0367979 (51:4221)
  • [5] S. Lang, Algebra, Addison-Wesley, Reading, Mass., 1965. MR 0197234 (33:5416)
  • [6] F. P. Peterson, The $ \mod p$ homotopy type of BSO and $ F/PL$, Bol. Soc. Mat. Mexicana 14 (1969), 22-27. MR 0259911 (41:4540)
  • [7] C. Wilkerson, Classifying spaces, Steenrod operations and algebraic closure, Topology 16 (1977), 227-237. MR 0442932 (56:1307)
  • [8] A. Zabrodsky, Hopf spaces, North-Holland, Amsterdam, 1976. MR 0440542 (55:13416)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0801344-3
Keywords: Classifying spaces, Steenrod operations, modular representations
Article copyright: © Copyright 1985 American Mathematical Society

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