Résumé : In 2019 J. Belk and B. Forrest introduced the family of Rearrangement Groups. These are groups of certain “piecewise-canonical” homeomorphisms of fractals that act by permuting the self-similar pieces that make up the fractal.
The family of rearrangement groups is a generalization of the main trio of Thompson groups F, T and V, each of which has made its appearance in many different topics: the groups T and V were the first examples of infinite finitely presented simple groups, whereas the fame of its smaller sibling F mostly originates from the decades-old open question regarding its possible amenability.
This talk will introduce Thompson groups and Rearrangement Groups, highlighting some known facts about them, such as the simplicity of commutator subgroups in many examples, a general result about invariable generation and a method to tackle the conjugacy problem.