 

Claire Wladis
Thompson's group F(n) is not minimally almost convex


Published: 
December 13, 2007

Keywords: 
Thompson's group, almost convexity 
Subject: 
20F65 


Abstract
We prove that Thompson's group F(n) is not minimally almost
convex with respect to the standard finite generating set. A group G with Cayley graph Γ is not minimally almost convex if for
arbitrarily large values of m there exist
elements g,h∈ B_{m} such that d_{Γ}(g,h)=2 and d_{Bm}(g,h)=2m.
(Here B_{m} is the ball of radius m centered at the identity.) We use treepair diagrams to represent elements of F(n) and then use
Fordham's metric to calculate geodesic length of elements of F(n). Cleary and Taback have shown that F(2) is not almost
convex and Belk and Bux have shown that F(2) is not minimally
almost convex; we generalize these results to show that F(n) is
not minimally almost convex for all n∈{2,3,4,...}.


Author information
Department of Mathematics, Borough of Manhattan Community College/City University of New York, 199 Chambers St., New York, NY 10007
cwladis@gmail.com

