Incoherence of free-by-free and surface-by-free groups

Robert Kropholler, Stefano Vidussi, Genevieve Walsh

Let $G$ be the semidirect product $\Gamma ⋊F_2$ where $\Gamma$ is either the free group $F_n$, $n>1$ or the fundamental group $S_g$ of a closed surface of genus $g>1$. We prove tha…