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math.GR2024
Eventually Self-Similar Groups acting on Fractals
Davide Perego, Matteo Tarocchi
Generalizing work by Belk and Forrest, we develop almost expanding hyperedge replacement systems that build fractal topological spaces as quotients of edge shifts under certain ``g…
math.GR2024
Rearrangement Groups of Fractals: Structure and Conjugacy
Matteo Tarocchi
This dissertation is about rearrangement groups: a class of groups of homeomorphisms of fractal topological spaces. Introduced in 2019 by J. Belk and B. Forrest, this class general…
math.GR2024
Rational Gluing in Edge Replacement Systems
Davide Perego, Matteo Tarocchi
In this paper, we prove the rationality of the gluing relation of edge replacement systems, which were introduced for studying rearrangement groups of fractals. More precisely, we…