Homotopy Theory

Abstract

Let X be a space and let x ₀ be a point in X. In section 2.1 we introduced the fundamental group $\pi _{1}(X,x_{0})$. In this chapter we introduce the homotopy groups $\pi _{n}(X,x_{0})$ for every n ≥ 0. Also, if (X, A, x ₀) is a triple, i.e., if A is a subspace of X and x ₀ is a point in A, we have the relative homotopy groups $\pi _{n}(X,A,x_{0})$ for every n ≥ 1.