Automorphisms of three-dimensional handlebodies

This paper gives a classification up to isotopy of automorphisms (self-homeomorphisms) of three-dimensional handlebodies and compression bodies, analogous to the Nielsen–Thurston classification of automorphisms of surfaces. Indecomposable automorphisms analogous to pseudo-Anosov automorphisms are identified and called generic. The first steps are taken towards understanding generic automorphisms using invariant laminations. An automorphism f : M→M of an arbitrary compact, connected, orientable, irreducible 3-manifold M with non-empty boundary can be understood by decomposing the 3-manifold into f-invariant submanifolds including the Jaco-Shalen–Johannson characteristic manifold and Bonahonʹs characteristic compression body.