Document Type
Article
Publication Date
2-1-2009
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. © 2008 American Mathematical Society Reverts to public domain 28 years from publication.
Recommended Citation
Burillo, José; Cleary, Sean; Stein, Melanie; and Taback, Jennifer, "Combinatorial and metric properties of Thompson's group t" (2009). Mathematics Faculty Publications. 56.
https://digitalcommons.bowdoin.edu/mathematics-faculty-publications/56