Properties of the Homotopy Groups

Abstract

In this chapter we shall demonstrate some of the elementary properties of the homotopy groups. Then we shall construct the relative homotopy groups π n (X, A, x0) of a pointed topological pair x0 ∈ A ⊂ X and show how they fit into a long exact sequence with the groups π n (A, x0) and π n (X, x0). Finally we shall discuss the relation between the groups π n (X, x0) and π n (X, x1) for different base points.