Metrics and embeddings of generalizations of Thompson's group

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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

The distance from the origin in the word metric for generalizations of Thompson's group is quasi-isometric to the number of carets in the reduced rooted tree diagrams representing the elements of . This interpretation of the metric is used to prove that every admits a quasi-isometric embedding into every , 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

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