Thompson-like groups acting on fractals

Matteo Tarocchi (University of Milano-Bicocca)

Monday 6th February 16:00-17:00 Maths 311B


Introduced in the '60s by Richard Thompson, each of the three Thompson groups F, T and V 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.

In 2019 J. Belk and B. Forrest introduced a generalization of Thompson groups, the family of rearrangement groups. These are groups of certain homeomorphisms of fractals that act by permuting the self-similar pieces that make up the fractal. This talk will introduce Thompson groups and rearrangement groups, highlighting some known facts about them, such as the simplicity of the commutator subgroups of the basilica and airplane rearrangement groups and a general result about invariable generation.

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