Fibrations and Homotopy Groups

  • Albert S. Schwarz
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 308)


The theory of fibrations is a very useful tool in the determination of homotopy groups. For a fibration (E,B,F,p), there is a relationship between the homotopy groups of E, B and F, and this often allows us to determine the homotopy of one of these spaces, given that of the others. In this chapter we will formulate particular cases of this relationship, and show how they can be used in the computation of homotopy groups of specific spaces. Later we will see how to derive these particular cases from a single general theorem—the theorem on the exact homotopy sequence of fibrations, which we prove in Section 11.2.


Unitary Transformation Homotopy Class Total Space Orbit Space Homotopy Group 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Albert S. Schwarz
    • 1
  1. 1.Department of Mathematics 565 Kerr HallUniversity of CaliforniaDavisUSA

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