Eventually Self-Similar Groups acting on Fractals
| Autor: | Perego, Davide, Tarocchi, Matteo |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 ``gluing'' equivalent relations. We define ESS groups, which are groups of homeomorphisms of these spaces that act as a finitary asynchronous transformations followed by self-similar ones, akin to the action of Scott-R\"{o}ver-Nekrashevych groups on the Cantor space. We provide sufficient conditions for finiteness properties of such groups, which allow us to show that the airplane and dendrite rearrangement groups have type $F_\infty$, that a group combining dendrite rearrangements and the Grigorchuk group is finitely generated, and that certain ESS groups of edge shifts have type $F_\infty$ (partially addressing a question of Deaconu), in addition to providing new proofs of previously known results about several Thompson-like groups. Comment: 40 pages |
| Databáze: | arXiv |
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