2022/04/05 by Jay, Magali
#28D15 (Secondary) #37E05 (Primary) 20E07 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2204.02456
We study the group of all interval exchange transformations (IETs). We show that for every IET S, there exists a dense open set of admissible IETs that share a relation with S. 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.