Twisted conjugacy classes in R. Thompson's group F

TL;DR

This paper proves that every automorphism of R. Thompson's group F has infinitely many twisted conjugacy classes, highlighting a significant property of the group's automorphisms and their Reidemeister numbers.

Contribution

It establishes that all automorphisms of R. Thompson's group F have infinitely many twisted conjugacy classes, combining existing results with elementary properties of the group.

Findings

All automorphisms of F have infinite Reidemeister number

The result leverages prior work by Matthew Brin

Uses elementary properties of Thompson's group F

Abstract

In this short article, we prove that any automorphism of the R. Thompson's group $F$ has infinitely many twisted conjugacy classes. The result follows from the work of Matthew Brin, together with a standard facts on R. Thompson's group $F$, and elementary properties of the Reidemeister numbers.