Centralizers in R. Thompson's group V_n
Collin Bleak, Hannah Bowman, Alison Gordon, Garrett Graham, Jacob, Hughes, Francesco Matucci, Jenya Sapir

TL;DR
This paper analyzes the structure of centralizers in Higman-Thompson groups V_n, revealing they are finitely generated and providing insights into the group's algebraic properties using tree pair techniques.
Contribution
It introduces a detailed analysis of centralizers in V_n using revealing tree pairs and derives that these centralizers are finitely generated, advancing understanding of the group's structure.
Findings
Centralizers in V_n are finitely generated.
Cyclic groups are undistorted in V_n.
Analysis uses revealing tree pairs and discrete train tracks.
Abstract
Let n be bigger than 1 and let A be an element in the Higman-Thompson group V_n. We study the structure of the centralizer of a in V_n through a careful analysis of the action of the group generated by A on the Cantor set C. We make use of revealing tree pairs as developed by Brin and Salazar from which we derive discrete train tracks to assist us in our analysis. A consequence of our structure theorem is that centralizers are finitely generated. Along the way we give a short argument using revealing tree pairs which shows that cyclic groups are undistorted in V_n.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Topological and Geometric Data Analysis
