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Transactions of the American Mathematical Society

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Self-maps of loop spaces. II


Authors: H. E. A. Campbell, F. R. Cohen, F. P. Peterson and P. S. Selick
Journal: Trans. Amer. Math. Soc. 293 (1986), 41-51
MSC: Primary 55P47; Secondary 55P10, 55P35, 55P45
DOI: https://doi.org/10.1090/S0002-9947-1986-0814911-3
MathSciNet review: 814911
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Abstract: We study under what conditions on a finite CW complex $ X$ is $ Q(X)$ atomic.


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  • [1] J. F. Adams, The Kahn-Priddy Theorem, Proc. Cambridge Philos. Soc. 73 (1973), 45-55. MR 0310878 (46:9976)
  • [2] H. E. A. Campbell, F. R. Cohen, F. P. Peterson and P. S. Selick, The space of maps of Moore spaces into spheres, Ann. of Math. Studies (to appear). MR 921473 (89a:55012)
  • [3] H. E. A. Campbell, F. P. Peterson and P. S. Selick, Self-maps of loop spaces. I, Trans. Amer. Math. Soc. 293 (1986), 1-39. MR 814910 (87e:55010a)
  • [4] F. R. Cohen, Splitting certain suspensions via self-maps, Illinois J. Math. 20 (1976), 336-347. MR 0405412 (53:9205)
  • [5] -, Orders of certain compositions, Canad. Math. Soc. Conf. Proc., vol. 2, 1982, pp. 289-295. MR 686122 (84f:55011)
  • [6] -, The unstable decomposition of $ {\Omega ^2}{\Sigma ^2}X$ and its applications, Math. Z. 182 (1983), 553-568. MR 701370 (85d:55008)
  • [7] -, Two-primary analogues of Selick's Theorem and the Kahn-Priddy Theorem for the $ 3$-sphere, Topology 23 (1984), 401-421. MR 780733 (86e:55020)
  • [8] F. R. Cohen, J. C. Moore and J. A. Neisendorfer, Exponents in homotopy theory, Ann. of Math. Studies (to appear). MR 921471 (89d:55035)
  • [9] -, Homology and James-Hopf invariants (unpublished).
  • [10] F. R. Cohen and J. A. Neisendorfer, A construction of $ p$-local $ H$-spaces, Lecture Notes in Math., vol. 1051, Springer-Verlag, Berlin and New York, 1984, pp. 351-359. MR 764588 (86e:55011)
  • [11] N. Jacobson, Lie algebras, Interscience, New York, 1962. MR 0143793 (26:1345)
  • [12] I. M. James, Cross-sections of Stiefel manifolds, Proc. London Math. Soc. 8 (1958), 536-547. MR 0100840 (20:7268)
  • [13] -, The topology of Stiefel manifolds, London Math. Soc. Lecture Note Series, no. 24, Cambridge Univ. Press, Cambridge, 1976. MR 0431239 (55:4240)
  • [14] D. S. Kahn and S. B. Priddy, Applications of the transfer to stable homotopy theory, Bull. Amer. Math. Soc. 78 (1972), 981-987. MR 0309109 (46:8220)
  • [15] -, The transfer and stable homotopy theory, Math. Proc. Cambridge Philos. Soc. 83 (1978), 103-111. MR 0464230 (57:4164b)
  • [16] P. Loeffler and N. Ray, A geometric proof of a theorem of Kahn and Priddy, J. London Math. Soc. 24 (1981), 329-334. MR 631944 (83c:55007)
  • [17] J. C. Moore, Séminaire Henri Cartan, 1954/55, École Norm. Sup.
  • [18] G. Segal, The stable homotopy of complex projective space, Quart. J. Math. Oxford Ser. (2) 24 (1973), 1-5. MR 0319183 (47:7729)

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DOI: https://doi.org/10.1090/S0002-9947-1986-0814911-3
Article copyright: © Copyright 1986 American Mathematical Society

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