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.Comment: 19 pages, 7 figure