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Metrics and embeddings of generalizations of Thompson's group $F$

Authors: J. Burillo, S. Cleary and M. I. Stein
Journal: Trans. Amer. Math. Soc. 353 (2001), 1677-1689
MSC (2000): Primary 20F65; Secondary 20F05, 20F38, 20E99, 05C25
Published electronically: December 18, 2000
MathSciNet review: 1806724
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Abstract | References | Similar Articles | Additional Information


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.

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Additional Information

J. Burillo
Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08192 Barcelona, Spain
Address at time of publication: Department of Applied Mathematics, University Politecnica de Catalunya, Campus Nord, Jordi Girona 1, 08034 Barcelona, Spain

S. Cleary
Affiliation: Department of Mathematics, City College of CUNY, New York, New York 10031

M. I. Stein
Affiliation: Department of Mathematics, Trinity College, Hartford, Connecticut 06106

Received by editor(s): September 25, 1998
Received by editor(s) in revised form: August 11, 1999
Published electronically: December 18, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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