Splittings of mapping tori of free group automorphisms

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We 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. Dedicata

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