Automorphisms of 3-Dimensional Handlebodies

This paper gives a classification up to isotopy of automorphisms (self-homeomorphisms) of 3-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 Bonahon’s characteristic compression body.