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

2023/12/31 by Baker, Krystofer, Savchuk, Dmytro
#20F65 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2401.00404

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× F and can thus be generated by 4 explicit elements. We show that the stabilizer of every non-dyadic rational point b∈ (0,1) is generated by 5 elements that are explicitly calculated as words in generators x₀, x₁ 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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• Towards computing the rational homology and assembly maps of generalised Thompson groups