Let $S$ be an orientable surface with negative Euler characteristic. Can somebody provide a reference for the following well-known results:
the cyclic subgroup generated by a pseudo-Anosov element in the mapping class $MCG(S)$ is undistorted in the mapping class group.
the cyclic subgroup generated by a Dehn twist of the mapping class group is undistorted.
$\pi_1(S)$ is exponentially distorted in the mapping class group.
Thank you in advance.