  A complex of incompressible surfaces in a handlebody is constructed so that
it contains, as a subcomplex, the complex of curves of the boundary of the
handlebody. For genus 2 handlebodies, the group of automorphisms of this
complex is used to characterize the mapping class group of the handlebody. In
particular, it is shown that all automorphisms of the complex of incompressible
surfaces are geometric, that is, induced by a homeomorphism of the handlebody.
