We describe some of the geometric properties of the automorphism group of Thompson’s group . We give realizations of geometrically via periodic tree pair diagrams, which lead to natural presentations and give effective methods for estimating the word length of elements. We study some natural subgroups of and their metric properties. In particular, we show that the subgroup of inner automorphisms of is at least quadratically distorted in , whereas other subgroups of isomorphic to are undistorted.
Cite this article
José Burillo, Sean Cleary, The automorphism group of Thompson’s group : subgroups and metric properties. Rev. Mat. Iberoam. 29 (2013), no. 3, pp. 809–828DOI 10.4171/RMI/741