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

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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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© 1972 Springer-Verlag Berlin Heidelberg

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Bousfield, A.K., Kan, D.M. (1972). A glimpse at the R-completion of non-nilpotent spaces. In: Homotopy Limits, Completions and Localizations. Lecture Notes in Mathematics, vol 304. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38117-4_7

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  • DOI: https://doi.org/10.1007/978-3-540-38117-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06105-2

  • Online ISBN: 978-3-540-38117-4

  • eBook Packages: Springer Book Archive