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arXiv · 1510.03133

Rearrangement groups of fractals

James Belk·Bradley Forrest
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Abstract

We construct rearrangement groups for edge replacement systems, an infinite class of groups that generalize Richard Thompson's groups F, T, and V . Rearrangement groups act by piecewise-defined homeomorphisms on many self-similar topological spaces, among them the Vicsek fractal and many Julia sets. We show that every rearrangement group acts properly on a locally finite CAT(0) cubical complex, and we use this action to prove that certain rearrangement groups are of type F infinity.

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James Belk, Bradley Forrest. 2015-10-12. Rearrangement groups of fractals. https://doi.org/10.1090/tran%2F7386

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