Haken will develop an improved version of the theory of normal-surfaces, making use of his recently proved splitting theorem and the polynomially bounded time demand of the Whitehead-Zieschang algorithms for simplifying meridian systems in handlebodies. This is expected to yield fast algorithms for determining distinguished cell-partitions for all those compact 3-manifolds whose first Betti number is greater than zero and which are known to be irreducible. In particular, it is expected to yield a fast algorithm of which it can be proved that it recognizes every trivial knot which is given in an arbitrary ambient 3-manifold. He will also continue his search for interesting examples of Heegaard diagrams of 3-manifolds.
