Basic Algebraic Topology

Chapter 11 Homology of Fibre Spaces

As indicated in the introduction to Chapter 1, the concept of fibration plays a central role in algebraic topology. However, apart from studying some special cases, viz., the covering projection in Chapter 2, a little bit about vector bundles in Chapter 5 and establishing the homotopy exact sequence of a fibration in Chapter 7, we have not studied much about fibrations so far. In this chapter, let us take up the ever-so-important study of fibrations again and go one step further. In Section 11.1, we shall deal with some generalities of fibrations. In Section 11.2, we shall discuss fibrations with fibres homotopy type of a sphere and establish Thom isomorphism theorem and, as an immediate consequence, the Gysin ...