Definition:Trivial Free Homotopy Class of Path

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $f: \closedint 0 1 \to S$ be a path in $T$.

Suppose $f$ is a constant path.

Then the free homotopy class of $f$ is called the trivial free homotopy class (of $f$).

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 6$: Geodesics and Distance. Closed Geodesics