I am currently reading Mapping Class Groups from the lecture note https://massuyea.perso.math.cnrs.fr/notes/formality.pdf. Now, on page 22, I got this highlighted line.
Is there any reference to this line? I know a very particular case, namely,
Let $α$ and $β$ be two essential simple closed curves in a surface $S$. Then $α$ is isotopic to $β$ if and only if $α$ is homotopic to $β$. This is Proposition $1.10$ in "A Primer on Mapping Class Groups" written by Benson Farb and Dan Margalit.
Any help will be appriceted. Thanks in advance.