Abstract
In this chapter we establish the following simple and useful sufficient conditions on a tower of fibrations {Ys}, in order that it can be used to obtain the homotopy type of the R-completion of a given space X:
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(i)
If f: X → {Ys is a map which induces, for every R-module M, an isomorphism
$$\mathop {\lim }\limits_ \to H*\left( {{Y_S};M} \right) \approx H*\left( {X;M} \right)$$then f induces a homotopy equivalence \({R_\infty }X \simeq \mathop {\lim }\limits_ \to {R_\infty }{Y_S}\).
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(ii)
If, in addition, each Ys is R-complete (Ch.I, 5.1) , then the space \(\mathop {\lim }\limits_ \to {Y_S}\) already has the same homotopy type as R∞X.
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(iii)
If, in addition, each Ys satisfies the even stronger condition of being R-nilpotent (4.2), then, in a certain precise sense, the tower {Ys} has the same homotopy type as the tower {Rs}
The online version of the original chapter can be found at http://dx.doi.org/10.1007/978-3-540-38117-4_3
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© 1972 Springer-Verlag Berlin Heidelberg
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Bousfield, A.K., Kan, D.M. (1972). Erratum to: Tower lemmas. In: Homotopy Limits, Completions and Localizations. Lecture Notes in Mathematics, vol 304. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38117-4_14
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DOI: https://doi.org/10.1007/978-3-540-38117-4_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06105-2
Online ISBN: 978-3-540-38117-4
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