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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)

Abstract

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.

Keywords

Fundamental Group Spectral Sequence Homotopy Type Homotopy Group Perfect Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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