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 , there exists a dense open set of admissible IETs that share a relation with . 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