Rearrangement groups of fractals

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.

Published version

References in corpus (1)

• Röver's Simple Group is of Type $F_{\infty }$

Cited by in corpus (7)

• Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson's and Houghton's groups
• Twisted Brin-Thompson groups
• Almost-automorphisms of trees, cloning systems and finiteness properties
• Generation and Simplicity in the Airplane Rearrangement Group
• A Class of Rearrangement Groups that are not Invariably Generated
• Hyperbolic and cubical rigidities of Thompson's group V
• Asymptotically rigid mapping class groups II: strand diagrams and nonpositive curvature