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arXiv · 2401.00404

Explicit Generators for the Stabilizers of Rational Points in Thompson's Group $F$

Krystofer Baker·Dmytro Savchuk
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Abstract

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.

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BibTeXRIS

Krystofer Baker, Dmytro Savchuk. 2024-11-20. Explicit Generators for the Stabilizers of Rational Points in Thompson's Group $F$. https://arxiv.org/abs/2401.00404

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