The fundamental group
From Maths
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[1]
- [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.
Theorem: [ilmath]\pi_1(X,x_0)[/ilmath] with the binary operation [ilmath]*[/ilmath] forms a group[2]
