In this paper, we study distortion in the group of affine interval exchange transformations (AIET). We prove that any distorted element of has an iterate that is conjugate by an element of to a product of infinite order restricted rotations, with pairwise disjoint supports. As consequences, we prove that no Baumslag–Solitar group, BS with , acts faithfully by elements of ; every finitely generated nilpotent group of is virtually abelian and there is no distortion element in , the subgroup of consisting of rational AIETs.
Cite this article
Nancy Guelman, Isabelle Liousse, Distortion in groups of affine interval exchange transformations. Groups Geom. Dyn. 13 (2019), no. 3, pp. 795–819DOI 10.4171/GGD/505