Document Type
Article
Publication Date
12-1-2003
Abstract
We show that Thompson's group F does not satisfy Cannon's almost convexity condition AC(n) for any positive integer n with respect to the standard generating set with two elements. To accomplish this, we construct a family of pairs of elements at distance n from the identity and distance 2 from each other, which are not connected by a path lying inside the n-ball of length less than k for increasingly large k. Our techniques rely upon Fordham's method for calculating the length of a word in F and upon an analysis of the generators' geometric actions on the tree pair diagrams representing elements of F. © 2003 Elsevier Inc. All rights reserved.
Recommended Citation
Cleary, Sean and Taback, Jennifer, "Thompson's group F is not almost convex" (2003). Mathematics Faculty Publications. 63.
https://digitalcommons.bowdoin.edu/mathematics-faculty-publications/63