Melanie Stein, Trinity College

Abstract:
Almost convexity of a group with finite generating set is equivalent to the existence of a tame 1-combing with tameness function ρ(n) = n. Thompson’s group F is not almost convex, so one could not hope for such a combing. We describe the next best thing: a tame 1-combing for F , with respect to the standard two generators, which satisfies a linear radial tameness function. Since F is not even minimally almost convex, this provides an example showing that even a relatively strong tameness condition does not imply the weakest of convexity conditions. (Joint work with Sean Cleary, Susan Hermiller, and Jennifer Taback.)