Combinatorial and metric properties of Thompson's group T

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

2005-03-29

arxiv.org/abs/math/0503670v2

Mathematics

Group Theory

21 pages, 9 figures, corrects results in Section 5 and typos

Scientific paper

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, and that F is undistorted in T. We describe how to recognize torsion elements in T.

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