IUMJ

Title: $PSL(2,\mathbb{Z})$ as a non-distorted subgroup of Thompson's group T

Authors: Ariadna Fossas

Issue: Volume 60 (2011), Issue 6, 1905-1926

Abstract:

In this paper we characterize the elements of $PSL_2(\mathbb{Z})$, as a subgroup of Thompson's group $T$, in the language of reduced tree pair diagrams and in terms of piecewise linear maps as well. Actually, we construct the reduced tree pair diagram for every element of $PSL_2(\mathbb{Z})$ in normal form. This allows us to estimate the length of the elements of $PSL_2(\mathbb{Z})$ through the number of carets of their reduced tree pair diagrams and, as a consequence, to prove that $PSL_2(\mathbb{Z})$ is a non-distorted subgroup of $T$. In particular, we find non-distorted free non-abelian subgroups of $T$.