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

Geometric quasi-isometric embeddings into Thompson's group F

Sean Cleary and Jennifer Taback

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 $\phi$ 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 $F^m \times \Z^n$, for integral $m,n \geq 0$, 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.
Both authors thank the referee for helpful comments.

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