Twisted conjugacy in fundamental groups of geometric $3$-manifolds

Abstract

A group $G$ has property $R_{\infty }$ if for every $\varphi \in Aut(G)$, there are an infinite number of $\varphi$-twisted conjugacy classes of elements in $G$. In this note, we determine the $R_{\infty }$-property for $G={\pi }_1(M)$ for all geometric $3$-manifolds $M$.

arXiv comment14 pages, no figures. The Main Theorem improved to cover all geometric 3-manifolds, errors and inaccuracies in v1 corrected,. exposition expanded and improved. To appear in Topology and its Applications