Twisted conjugacy in Richard Thompson's group T

Abstract

Let $f$ be an automorphism of a group $G$. Two elements $x, y$ in $G$ are said to be in the same $f$-twisted conjugacy class if there exists an element $z$ in $G$ such that $y=z x f(z^{-1})$. This is an equivalence relation known as $f$-twisted conjugacy. If the number $R(f)$ of $f$-twisted conjugacy classes is infinite for every automorphism $f$ of $G$ one says that $G$ has the $R_\infty$-property. We show that the Richard Thompson group $T$ has the $R_\infty$-property.