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Fibre lemmas

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

Abstract

For a general fibration of connected spaces F → E → B, the map RE → RB is always a fibration (Ch.I, 4.2), but RF need not have the same homotopy type as the fibre of RE → RB. For example, if R = Q, then
$${S^2} \to {P^2} \to K\left( {{Z_2},1} \right)$$
is, up to homotopy, a fibration, but RS2 → RP2 → RK(Z2,1) is not, because (Ch.I, 5.5) RP2 and RK(Z2,1) are contractible, while RS2 is not.

Keywords

Exact Sequence Spectral Sequence Short Exact Sequence Homotopy Type Connected Space 
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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