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arXiv · 2209.02300

On groups of rectangle exchange transformations

Yves Cornulier·Octave Lacourte
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Abstract

We study a generalization Rec_d of the group IET=Rec_1 of interval exchange transformations in every dimension d>0, called the rectangle exchange transformations group. The subset of restricted rotations in IET is a generating subset and we prove that a natural generalization of these elements, called restricted shuffles, form a generating subset of Rec_d. We denote by T_d the subset of Rec_d made up of those transformations that permute two disjoint rectangles by translations. We prove that the derived subgroup of Rec_d is generated by T_d. We also identify the abelianization of Rec_d.

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Yves Cornulier, Octave Lacourte. 2022-09-06. On groups of rectangle exchange transformations. https://arxiv.org/abs/2209.02300

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