Pure mapping class group of the four-punctured sphere
= Pure mapping class group of the four-punctured sphere
{title2=$\operatorname{PMod}(S_{0,4})\cong F_2$}
The <Birman exact sequence> and $\operatorname{PMod}(S_{0,3})=1$ identify $\operatorname{PMod}(S_{0,4})$ with $\pi_1(S_{0,3})$, the free group of rank two.