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

Daciberg Gonçalves, Parameswaran Sankaran, Peter Wong

Published 2020-03-17Version 1

A group $G$ has property $R_\infty$ if for every $\phi\in Aut(G)$, there are an infinite number of $\phi$-twisted conjugacy classes of elements in $G$. In this note, we determine the $R_\infty$-property for $G=\pi_1(M)$ for almost all geometric $3$-manifolds $M$. The only case that are left out are certain Sol manifolds which are torus bundles.