Fibrations and Homotopy Groups

Abstract

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.