Rigidity of cusp-decomposable manifolds

Cusp-decomposable manifolds form a large class of manifolds that
are not locally homogeneous and generally do not admit a nonpositively
curved metric, but smooth rigidity holds within this class of manifolds. I
will define cusp-decomposable manifolds and prove that they are smoothly
rigid within this class. I will also prove that the group of outer
automorphisms of the fundamental group of such manifolds is an extension
of an abelian group by a finite group. Elements of the abelian group are
induced by diffeomorphisms that are analogous to Dehn twists in surface
topology. This gives a simple description of self-diffeomorphisms of
cusp-decomposable manifolds up to homotopy.