Spectral Sequences and Homotopy Groups of Spheres

Abstract

the technique of obstruction theory developed in the last chapter focuses attention on the computation of homotopy groups. In this chapter we obtain some results about the homotopy groups of spheres. The method we follow is due to Serre1 and uses the technical tool known as a spectral sequence. This algebraic concept is introduced for the study of the homology and cohomology properties of arbitrary fibrations, but it has other important applications in algebraic topology, and the number of these is constantly increasing. Some indication of the power of spectral sequences will be apparent from the results obtained by its use here.