4 papers
Limit spaces of vertex and edge replacement systems
Davide Perego, Matteo Tarocchi
We introduce and study VERSs (vertex and edge replacement systems) as a technology of graph expansions. We consider its history graph, an augmented tree that records each graph exp…
Orderable Thompson-like groups arising from Ore categories
Davide Perego, Matteo Tarocchi
We give sufficient conditions for left- and bi-orderability of fundamental groups of Ore categories in terms of indirect factors, including Thompson groups and many of their genera…
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…
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…