2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61743We present necessary and sufficient conditions for the existence of a splitting over $\mathbb{Z}$ of the mapping torus $M_ϕ=F\rtimes \mathbb{Z}$ of a free group automorphism $ϕ$.16 pages, 6 figures, revised according to referee's suggestions To appear in Geom. DedicataGroup Theory37E30text