Explicit generators for the stabilizers of rational points in Thompson’s group F

We construct explicit finite generating sets for the stabilizers in Thompson’s group F of rational points of a unit interval or the 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.