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A whitehead theorem for long towers of spaces

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Abstract

We show that one can construct the universalR-homology isomorphismK →E RX of Bousfield [1] by a transfinite iteration of an elementary homology correction map. This correction map is essentially the same as the one used classically to define Adams spectral sequence. This yields a topological characterization of the class of local spaces as the smallests containingK(A, n)’s and closed under homotopy inverse limit.

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References

  1. A. K. Bousfield,The localization of spaces with respect to homology, Topology14(1975), 135–150.

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  2. A. K. Bousfield,Homological localization towers for groups and π-modules, to appear.

  3. A. K. Bousfield and D. M. Kan,Homotopy Limits, Completion and Localizations, Lecture Notes in Math. No. 304, Springer, New York, 1972.

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  4. E. Dror and W. G. Dwyer,A long homology localization tower, to appear in Comment. Math. Helv.

  5. K. Lamotke,Semisimpliziale algebraische Topologie, Springer, New York, 1968.

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  6. J. P. May,Simplicial Objects in Algebraic Topology, Van Nostrand, Princeton, 1967.

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Authors and Affiliations

  1. The Hebrew University of Jerusalem, Jerusalem, Israel

    E. Dror & W. G. Dwyer

  2. Yale University, New Haven, Connecticut, USA

    E. Dror & W. G. Dwyer

Authors
  1. E. Dror
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  2. W. G. Dwyer
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Additional information

This research was partially supported by the National Science Foundation, Grant # MCS76-08795, and by the U.S.-Israel Bi-National Science Foundation Grant # 680.

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Dror, E., Dwyer, W.G. A whitehead theorem for long towers of spaces. Israel J. Math. 29, 141–154 (1978). https://doi.org/10.1007/BF02762004

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  • DOI: https://doi.org/10.1007/BF02762004

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