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arXiv · 2204.02456

Relations with a fixed interval exchange transformation

Magali Jay
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Abstract

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.

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Magali Jay. 2022-04-05. Relations with a fixed interval exchange transformation. https://arxiv.org/abs/2204.02456

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