English

Relations with a fixed interval exchange transformation

Group Theory 2023-12-08 v2 Dynamical Systems

Abstract

We study the group of all interval exchange transformations (IETs). We show that for every IET SS, there exists a dense open set of admissible IETs that share a relation with SS. This is an extension of a result published by Dahmani, Fujiwara and Guirardel in 2013: the group generated by a generic pair of elements of IET([0;1[) is not free (assuming a suitable condition on the underlying permutation). Key words: interval exchange transformations, free group of rank 2, interval exchange transformations with flips.

Keywords

Cite

@article{arxiv.2204.02456,
  title  = {Relations with a fixed interval exchange transformation},
  author = {Magali Jay},
  journal= {arXiv preprint arXiv:2204.02456},
  year   = {2023}
}

Comments

14 pages, 7 figures

R2 v1 2026-06-24T10:39:03.760Z