Distortion in the group of circle homeomorphisms

Abstract

Let $G$ be the group ${\mathrm{PAff}}_{+}({\mathbf{S}}^1)$ of piecewise--affine circle homeomorphisms or the group ${\Diff}^{\infty}(\mathbb R/\mathbb Z)$ of smooth circle diffeomorphisms. A constructive proof that all irrational rotations are distorted in $G$ is given.

4 pages