The fundamental group

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

Definition

Given a topological space $X$ and a point $x_0\in X$ the fundamental group is

• $$\pi_1(X,x_0)$$ denotes the set of homotopy classes of loops based at $x_0$

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