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

 

Combinatorial and metric properties of Thompson's group $ T$


Authors: José Burillo, Sean Cleary, Melanie Stein and Jennifer Taback
Journal: Trans. Amer. Math. Soc. 361 (2009), 631-652
MSC (2000): Primary 20F05; Secondary 20F65, 20E32
Published electronically: September 26, 2008
MathSciNet review: 2452818
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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$.


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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

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04381-X
PII: S 0002-9947(08)04381-X
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.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.