New York Journal of Mathematics
Volume 9 (2003) 141-148


Sean Cleary and Jennifer Taback

Geometric quasi-isometric embeddings into Thompson's group F

Published: September 10, 2003
Keywords: Thompson's group F, quasi-isometric embeddings
Subject: 20F32

We use geometric techniques to investigate several examples of quasi-isometrically embedded subgroups of Thompson's group F. Many of these are explored using the metric properties of the shift map φ in F. These subgroups have simple geometric but complicated algebraic descriptions. We present them to illustrate the intricate geometry of Thompson's group F as well as the interplay between its standard finite and infinite presentations. These subgroups include those of the form Fm×Zn, for integral m,n ≧ 0, which were shown to occur as quasi-isometrically embedded subgroups by Burillo and Guba and Sapir.


The first author acknowledges support from PSC-CUNY grant #63438-0032.

The second author acknowledges partial support from an NSF-AWM Mentoring Travel Grant and would like to thank the University of Utah for its hospitality during the writing of this paper.

Author information

Sean Cleary:
Department of Mathematics, City College of New York, City University of New York, New York, NY 10031

Jennifer Taback:
Department of Mathematics and Statistics, University at Albany, Albany, NY 12222