Advertisement

Erratum to: Tower lemmas

  • Aldridge K. Bousfield
  • Daniel M. Kan
Part of the Lecture Notes in Mathematics book series (LNM, volume 304)

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:
  1. (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 \({R_\infty }X \simeq \mathop {\lim }\limits_ \to {R_\infty }{Y_S}\).
     
  2. (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 RX.

     
  3. (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}

     

Copyright information

© Springer-Verlag Berlin Heidelberg 1972

Authors and Affiliations

  • Aldridge K. Bousfield
    • 1
  • Daniel M. Kan
    • 2
  1. 1.Department of MathematicsUniversity of IllinoisChicagoUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations