Index

This shows a path homotopy between two loops in the torus
$T=S^1\times S^1$. The initial loop is $u*v$, where $u$ is the
horizontal red circle and $v$ is the vertical blue circle. By
sliding the slider we see that this is path homotopic to $v*u$.
(It is an unusual feature of the torus that $\pi_1(T)$ is
commutative. In most other spaces, $u*v$ would not be path
homotopic to $v*u$.)