Combinatorial and metric properties of Thompson’s group $T$
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- by José Burillo, Sean Cleary, Melanie Stein and Jennifer Taback PDF
- Trans. Amer. Math. Soc. 361 (2009), 631-652 Request permission
Abstract:
We discuss metric and combinatorial properties of Thompson’s group $T$, including normal forms for elements and unique tree pair diagram representatives. We relate these properties to those of Thompson’s group $F$ when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of $T$ arising from minimal factorizations of elements into natural pieces. We show that the number of carets in a reduced representative of an element of $T$ estimates the word length, that $F$ is undistorted in $T$, and we describe how to recognize torsion elements in $T$.References
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Additional Information
- José Burillo
- Affiliation: Departament de Matemática Aplicada IV, Universitat Politècnica de Catalunya, Escola Politècnica Superior de Castelldefels, 08860 Castelldefels, Barcelona, Spain
- Email: burillo@mat.upc.es
- Sean Cleary
- Affiliation: Department of Mathematics, The City College of New York & The CUNY Graduate Center, New York, New York 10031
- Email: cleary@sci.ccny.cuny.edu
- Melanie Stein
- Affiliation: Department of Mathematics, Trinity College, Hartford, Connecticut 06106
- Email: melanie.stein@trincoll.edu
- Jennifer Taback
- Affiliation: Department of Mathematics, Bowdoin College, Brunswick, Maine 04011
- Email: jtaback@bowdoin.edu
- Received by editor(s): March 25, 2005
- Received by editor(s) in revised form: July 24, 2006
- Published electronically: September 26, 2008
- Additional Notes: The first, second and fourth authors acknowledge support from NSF International Collaboration grant DMS-0305545 and are grateful for the hospitality of the Centre de Recerca Matemàtica.
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 631-652
- MSC (2000): Primary 20F05; Secondary 20F65, 20E32
- DOI: https://doi.org/10.1090/S0002-9947-08-04381-X
- MathSciNet review: 2452818