Quasi-isometric Embeddings from Generalised Thompson's Groups to Thompson's Group T

Brown has defined generalised Thompson's groups Fn, Tn, Vn where n is an integer at least 2 and Thompson's groups F = F2, T = T2, V = V2 in the 80's. Burillo, Cleary and Stein have found that there is a quasi-isometric embedding from Fn to Fm where n and m are positive integers at least 2. We show that there is a quasi-isometric embedding from Tn to T2 for any n > 2 and no embeddings from T2 to Tn for n > 3.

Automated summary

This article introduces the generalized Thompson's groups defined by Brown and the quasi-isometric embedding theorems found by Burillo, Cleary, and Stein. It shows that there exists a quasi-isometric embedding from Tn to T2 for any n > 2, but no embeddings from T2 to Tn for n > 3.