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

A group $G$ has property $R_\infty$ if for every $ϕ\in Aut(G)$, there are an infinite number of $ϕ$-twisted conjugacy classes of elements in $G$. In this note, we determine the $R_\infty$-property for $G=π_1(M)$ for all geometric $3$-manifolds $M$.

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