A glimpse at the R-completion of non-nilpotent spaces

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


Although the R-completion is quite well understood for nilpotent spaces (Ch.V and Ch.VI), the situation for non-nilpotent spaces is still very mysterious. So far we have essentially dealt with only one non-nilpotent example, in Ch.IV, 5.3, where we showed that for any free group F
$${R_\infty }K\left( {F,1} \right) \simeq K\left( {F_R^ \wedge ,l} \right)$$
and our main purpose in this chapter is to discuss some other non-nilpotent spaces and indicate how little is known about them and how much more work remains to be done for non-nilpotent spaces.


Fundamental Group Spectral Sequence Homotopy Type Homotopy Group Perfect Group 
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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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