A computable obstruction theory for existence and uniqueness of Seifert constructions with general homogeneous spaces as typical fiber, has been recently developed by Professors K.B. Lee and F. Raymond. Professor Raymond will refine this theory and develop geometric applications. In particular, the deformation theory of geometric structures that preserve the fiber structure will be studied for various Seifert fiberings and the topology of the corresponding moduli spaces will be investigated. Professor Scott will investigate further several problems centered about three important conjectures that relate the topology of 3-manifolds with their fundamental groups. Consider closed oriented irreducible 3-manifolds with infinite fundamental groups. If M and N are homotopically equivalent, are they homeomorphic? If the fundamental group contains a central subgroup isomorphic to the integers, is M a classical Seifert 3-manifold? Is the universal covering homeomorphic to Euclidean space? These topological investigations shed light on the ways in which geometric objects can be assembled from simpler geometric objects. Solution spaces to algebraic or differential equations give rise to these same objects, which makes their structural properties pervasive and understanding them important.
