p-completions of nilpotent spaces

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


In this chapter we discuss the p-completion, i.e. the “up to homotopy” version of the Zp-completion, for nilpotent spaces. It turns out that this p-completion is closely related to the p-profinite completion of [Quillen (PG)] and [Sullivan, Ch.3]; indeed, one can show that these completions coincide for spaces with Zp-homology of finite type, although they differ for more general spaces. The basic properties of p-profinite completions are well-known for simply connected spaces of finite type, and the main purpose of this chapter is to obtain similar results for p-completions of arbitrary nilpotent spaces.


Abelian Group Spectral Sequence Nilpotent Group Short Exact Sequence Finite Type 
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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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