Automorphisms of 3-dimensional handlebodies

This paper gives a classification up to isotopy of automorphisms (self-homeo-morphisms) of 3-dimensional handlebodies and compression bodies, analogous to the Nielsen-Thurston classification of automorphisms of surfaces. Indecom-posable automorphisms analogous to pseudo-Anosov automorphisms are identi-fied 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 Bonahon’s characteristic compression body