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 $y=zxf(z^{-1})$. 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.

Nine pages, no figures. There was an error in the statement of Theorem 2.1 which is corrected. A new reference has been added

References in corpus (2)

• Locally Moving Groups and the Reconstruction Problem for Chains and Circles
• The conjugacy problem in extensions of Thompson's group F

Cited by in corpus (5)

• The $R_{\infty }$ property for Houghton's groups
• The $R_{\infty }$ and $S_{\infty }$ properties for linear algebraic groups
• The $R_{\infty }$ property for nilpotent quotients of surface groups
• Twisted conjugacy in classical groups over certain domains of Characteristic $p>0$
• Automorphisms of the generalised Thompson's group $T_{n,r}$