Centralizers in R.Thompson's group V_n

Groups, Geometry and Dynamics, 7(4) (2013), 821–865
http://dx.doi.org/10.4171/GGD/207 (preprint - http://arxiv.org/abs/1107.0672)

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.