Claire Wladis

The Distortion of Thompson Groups in the Thompson-Stein groups

Abstract:
We embed the generalized Thompson groups of the form F(m) into the
Thompson-Stein groups of the form F(n_1,...,n_k) and show that each of these
groups, and therefore F itself, is exponentially distorted in F(n_1,...,n_k)
for k>1. This talk extends recent results for a smaller class of generalized
Thompson groups to all groups of the form F(m).

This result is the first known example of one Thompson-type group being
distorted inside another. Burillo, Cleary and Stein showed that F(n) is
quasi-isometrically embedded into F(m) for all integers n and m greater than
1, and Burillo, Cleary, Stein and Taback showed that F is
quasi-isometrically embedded in Thompson's group T.  Burillo, Cleary,
Taback, Guba, and Sapir have each given proofs using different methods
showing that F^n x Z^m is quasi-isometrically embedded in F for all integers
n and m greater than 1. Recent work of Burillo and Cleary has built on this
result by using the same method to prove that Thompson's groups F and V are
also distorted in the multidimensional Thompson's group nV.