The mapping class group of a Heegaard splitting of the 3-torus.

The mapping class group of a Heegaard splitting is the group
of (isotopy classes of) automorphisms of
the ambient 3-manifold that take the Heegaard surface onto itself. I
will describe a number of
elements of the mapping class group of a genus three Heegaard splitting
of the 3-torus and
outline the key points of a proof that these elements generate the
entire group.