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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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

Abstract:

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
Email: burillo@mat.upc.es

S. Cleary
Affiliation: Department of Mathematics, City College of CUNY, New York, New York 10031
Email: cleary@math0.sci.ccny.cuny.edu

M. I. Stein
Affiliation: Department of Mathematics, Trinity College, Hartford, Connecticut 06106
Email: mstein@mail.trincoll.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02650-7
PII: S 0002-9947(00)02650-7
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