Definition talk:Freely Homotopic Loops

Definition collision
I should point out that the definition of freely homotopic given by Lee is different from the definition Definition:Free Homotopy, which does not include the requirement that


 * $\forall t \in \closedint 0 1 : \map H {0, t} = \map H {1, t}$

The extra requirement of $H$ comes from the idea that for all $t \in \closedint 0 1$, the map $s \mapsto \map H {s,t}$ should itself be a loop. Of course, this only works when $H$ is a homotopy between two loops. This is why the general definition does not include this requirement.

We should find a way to separate these two definitions - maybe make a subpage to Definition:Free Homotopy, where we explain the difference between freely homotopic and freely homotopic loops. Any suggestions? --Anghel (talk) 23:53, 28 November 2022 (UTC)


 * Fiddly. The short answer is that we need to establish a source for Definition:Free Homotopy. --prime mover (talk) 06:26, 29 November 2022 (UTC)