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Splittings of mapping tori of free group automorphisms. (English) Zbl 1044.20010
Summary: We present necessary and sufficient conditions for the existence of a splitting over \(\mathbb{Z}\) of the mapping torus \(M_\phi=F\rtimes_\phi\mathbb{Z}\) of a free group automorphism \(\phi\).

MSC:
20E05 Free nonabelian groups
20E36 Automorphisms of infinite groups
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20E08 Groups acting on trees
20F67 Hyperbolic groups and nonpositively curved groups
37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
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