Metrics and embeddings of generalizations of Thompson’s group $F$
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- by J. Burillo, S. Cleary and M. I. Stein PDF
- Trans. Amer. Math. Soc. 353 (2001), 1677-1689 Request permission
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.References
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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
- Received by editor(s): September 25, 1998
- Received by editor(s) in revised form: August 11, 1999
- Published electronically: December 18, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 1677-1689
- MSC (2000): Primary 20F65; Secondary 20F05, 20F38, 20E99, 05C25
- DOI: https://doi.org/10.1090/S0002-9947-00-02650-7
- MathSciNet review: 1806724