Distance and subgruoups of Thompson's group F
by
José Burillo
Tufts University

Thompson's group F admits several representations as a group of some piecewise-linear homeomorphisms of the real line or of an interval. We will study how this models can be used to obtain some group-theoretical properties of F. A formula computing the word metric of F is found using one of these models, and it is used to obtain several results: the fact that the growth of F is exponential, the nondistortion of some interesting subgroups of F, and the asymptotic cone of F being infinite-dimensional.

Date received: March 5, 1998