Thompson's group F is not almost convex

Details Thompson's group F is not almost convex Thompson's group F is not almost convex

2002-04-19

arxiv.org/abs/math/0204249v1

Mathematics

Group Theory

19 pages, 7 figures

Scientific paper

We show that Thompson's group F does not satisfy Cannon's almost convexity condition AC(n) for any integer n in the standard finite two generator presentation. 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.

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