Walter Neumann will continue his study of the topology of complex curves and surfaces and their singularities, particularly the influence of the existence of complex structures on the topology and topological invariants of the associated 3- and 4-manifolds. He will also study geometric structures on real and complex manifolds in low dimensions, including singular structures, deformation of structures, their invariants, and arithmetic questions related to the invariants. Remarkable connections between geometry and algebra are uncovered at every turn. Basic to geometry and physics are 3- and 4-dimensional manifolds. Their topological properties are such fundamental things as connectedness and knottedness. It is impressive how effective algebraic techniques have been in investigating these properties.
