The automorphism group of Thompson's group F: subgroups and metric properties
Abstract
We describe some of the geometric properties of the automorphism group Aut(F) of Thompson's group F. We give realizations of 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) and their metric properties. In particular, we show that the subgroup of inner automorphisms of F is at least quadratically distorted in Aut(F), whereas other subgroups of Aut(F) isomorphic to F are undistorted.
 Publication:

arXiv eprints
 Pub Date:
 July 2011
 arXiv:
 arXiv:1107.4336
 Bibcode:
 2011arXiv1107.4336C
 Keywords:

 Mathematics  Group Theory;
 20F65;
 20E36
 EPrint:
 24 pages, 14 figures