JournalsrmiVol. 29, No. 3pp. 809–828

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

  • José Burillo

    Universitat Politècnica de Catalunya, Castelldefels, Spain
  • Sean Cleary

    The City College of CUNY, New York, USA
The automorphism group of Thompson’s group $F$: subgroups and metric properties cover

Abstract

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

Cite this article

José Burillo, Sean Cleary, The automorphism group of Thompson’s group FF: subgroups and metric properties. Rev. Mat. Iberoam. 29 (2013), no. 3, pp. 809–828

DOI 10.4171/RMI/741