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

Author
Burillo, J.; Cleary, S.
Type of activity
Journal article
Journal
Revista matemática iberoamericana
Date of publication
2013
Volume
29
Number
3
First page
809
Last page
828
DOI
https://doi.org/10.4171/RMI/741 Open in new window
Project funding
Métodos geométricos en teoría de grupos
URL
http://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=29&iss=3&rank=4 Open in new window
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 ...
Keywords
Thompson's group
Group of research
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics

Participants