Czechoslovak Mathematical Journal

, Volume 55, Issue 2, pp 465–470 | Cite as

Homomorphic images and rationalizations based on the Eilenberg-Maclane spaces

  • Dae-Woong Lee


Are there any kinds of self maps on the loop structure whose induced homomorphic images are the Lie brackets in tensor algebra? We will give an answer to this question by defining a self map of ΩΣK(\(\mathbb{Z}\), 2d), and then by computing efficiently some self maps. We also study the topological rationalization properties of the suspension of the Eilenberg-MacLane spaces. These results will be playing a powerful role in the computation of the same n-type problems and giving us an information about the rational homotopy equivalence.


Lie bracket tensor algebra rationalization Steenrod power 


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  1. [1]
    D. Lee and C. A. McGibbon: The same n-type problem for certain suspensions. Preprint.Google Scholar
  2. [2]
    B. Gray: Homotopy theory, an Introduction to Algebraic Topology. Academic Press, New York, 1975.Google Scholar
  3. [3]
    C. A. McGibbon: Self maps of projective spaces. Trans. Amer. Math. Soc. 271 (1982), 325–346.Google Scholar
  4. [4]
    C. A. McGibbon: Phantom maps. In: The Handbook of Algebraic Topology (I. M. James, ed.). North-Holland, New York, 1995.Google Scholar
  5. [5]
    K. Morisugi: Projective elements in K-theory and self maps of ΣℂP . J. Math. Kyoto Univ. 38 (1998), 151–165.Google Scholar
  6. [6]
    N. E. Steenrod and D. B. A. Epstein: Cohomology operations. Ann. of Math. Stud., No. 50. Princeton University Press, Princeton, 1962, pp. 139.Google Scholar
  7. [7]
    D. Sullivan: The genetics of homotopy theory and the Adams conjecture. Ann. of Math. 100 (1974), 1–79.Google Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2005

Authors and Affiliations

  • Dae-Woong Lee
    • 1
  1. 1.Department of MathematicsChonbuk National UniversityChonju, Chonbukthe Republic of Korea

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