This project includes research on the topological classification of hamiltonian systems, in particular the classification of trajectories, problems of classical mechanics and the dynamics of a rigid body; the relation to Seifert fibred spaces and graph manifolds; methods for calculating the cohomology of diffeomorphism groups and loop manifolds; the index theory of the Dirac-Ramon operator on loop manifolds, together with applications to quantum field theory; conditions for the existence of Bott functions whose singularities form a torus; conditions for the existence of a closed orbit in a hamiltonian system with a Bott function; the first obstruction to the topological equivalence of hamiltonian systems.

A further development of the computer analysis for classification problems will take place in low-dimensional topology, in the theory of integrable hamiltonian systems and of local minimal networks, and of some other problems concerning the topology of manifolds.