Metrics and embeddings of generalizations of Thompson's group F

Jose Burillo, Sean Cleary, Melanie Stein

Published 1998-09-30, updated 1998-12-14Version 3

The distance from the origin in the word metric for generalizations F(p) of Thompson's group F is quasi-isometric to the number of carets in the reduced rooted tree diagrams representing the elements of F(p). This interpretation of the metric is used to prove that every F(p) admits a quasi-isometric embedding into every F(q), and also to study the behavior of the shift maps under these embeddings.