Let F be a surface and suppose that \phi: F -> F is a pseudo-Anosov
homeomorphism fixing a puncture p of F. The mapping torus M = M_\phi\ is
hyperbolic and contains a maximal cusp C about the puncture p.
We show that the automorphism group of the disk complex is isomorphic to the
handlebody group. Using this, we prove that the outer automorphism group of the
handlebody group is trivial.
We show that the automorphism group of the disk complex is isomorphic to the
handlebody group. Using this, we prove that the outer automorphism group of the
handlebody group is trivial.