Explicit Generators for the Stabilizers of Rational Points in Thompson's Group $F$
| Autor: | Baker, Krystofer, Savchuk, Dmytro |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We construct explicit finite generating sets for the stabilizers in Thompson's group $F$ of rational points of a unit interval or a Cantor set. Our technique is based on the Reidemeister-Schreier procedure in the context of Schreier graphs of such stabilizers in $F$. It is well known that the stabilizers of dyadic rational points are isomorphic to $F\times F$ and can thus be generated by 4 explicit elements. We show that the stabilizer of every non-dyadic rational point $b\in (0,1)$ is generated by 5 elements that are explicitly calculated as words in generators $x_0, x_1$ of $F$ that depend on the binary expansion of $b$. We also provide an alternative simple proof that the stabilizers of all rational points are finitely presented. Comment: 19 pages, 9 figures and pictures |
| Databáze: | arXiv |
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