Definition:Fundamental Group

Definition

Let $\struct {X, x_0}$ be a pointed topological space with base point $x_0$.

The fundamental group $\map {\pi_1} {X, x_0}$ of $X$ at the base point $x_0$ is the set of homotopy classes of loops with base point $x_0$ with multiplication of homotopy classes of paths.

Also see

• Fundamental Group is Group
• Definition:Fundamental Group Functor
• Definition:Homotopy Group
• Fundamental Group is Independent of Base Point for Path-Connected Space

Sources

• 2000: James R. Munkres: Topology (2nd ed.): $9$: The Fundamental Group $\S 52$: The Fundamental Group