Conjugacy and dynamics in almost automorphism groups of trees
Abstract
We determine when two almost automorphisms of a regular tree are conjugate. This is done by combining the classification of conjugacy classes in the automorphism group of a level-homogeneous tree by Gawron, Nekrashevych and Sushchansky and the solution of the conjugacy problem in Thompson’s V by Belk and Matucci. We also analyze the dynamics of a tree almost automorphism as a homeomorphism of the boundary of the tree.
Communicated by A. Olshanskii