Groups and Dynamics Seminar

Date: April 17, 2024

Time: 3:00PM - 4:00PM

Location: BLOC 123

Speaker: Dmytro Savchuk, University of South Florida

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

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. This is a joint work with Krystofer Baker.