An R-completion of groups and its relation to the R-completion of spaces

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


In this chapter we introduce, for any solid (Ch.I, 4.5) ring R, an Artin-Mazur-like R-completion of groups and show that it can be used to construct, up to homotopy, the R-completion of spaces. The theoretical basis for this is in Chapter III, where we developed a flexible “tower lemma” approach to R-completions.


Simplicial Group Spectral Sequence Homotopy Type Inverse Limit Central Series 
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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

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