The fundamental group

Requires: Paths and loops in a topological space and Homotopic paths

Definition

Given a topological space [ilmath]X[/ilmath] and a point [ilmath]x_0\in X[/ilmath] the fundamental group is

• [math]\pi_1(X,x_0)[/math] denotes the set of homotopy classes of loops based at [ilmath]x_0[/ilmath]

forms a group under the operation of multiplication of the homotopy classes.