Centralizers in R. Thompson's group V_n
Group Theory
2011-09-14 v3 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.1107.0672,
title = {Centralizers in R. Thompson's group V_n},
author = {Collin Bleak and Hannah Bowman and Alison Gordon and Garrett Graham and Jacob Hughes and Francesco Matucci and Jenya Sapir},
journal= {arXiv preprint arXiv:1107.0672},
year = {2011}
}
Comments
32 pages, 18 figures. Added a reference in the introduction