The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Revista Matemática Iberoamericana


Full-Text PDF (279 KB) | Metadata | Table of Contents | RMI summary
Volume 29, Issue 3, 2013, pp. 809–828
DOI: 10.4171/RMI/741

Published online: 2013-08-04

The automorphism group of Thompson’s group $F$: subgroups and metric properties

José Burillo[1] and Sean Cleary[2]

(1) Universitat Politècnica de Catalunya, Castelldefels, Spain
(2) The City College of CUNY, New York, USA

We describe some of the geometric properties of the automorphism group $\operatorname {Aut}(F)$ of Thompson’s group $F$. We give realizations of $\operatorname {Aut}(F)$ 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 $\operatorname {Aut}(F)$ and their metric properties. In particular, we show that the subgroup of inner automorphisms of $F$ is at least quadratically distorted in $\operatorname {Aut}(F)$, whereas other subgroups of $\operatorname {Aut}(F)$ isomorphic to $F$ are undistorted.

Keywords: Thompson’s group

Burillo José, Cleary Sean: The automorphism group of Thompson’s group $F$: subgroups and metric properties. Rev. Mat. Iberoam. 29 (2013), 809-828. doi: 10.4171/RMI/741