The planned research focuses on some questions concerning the topology of singularities and various related structures. It includes a continuation of the investigator's study of the topology of isolated singularities using methods of surgery theory, an application of insights gathered from the study of algebraic knots to the study of fibered knots which leads to the definition of some new invariants, and an investigation of free and semi-free group actions on spheres for which the invariant submanifolds are links of singularities. In addition it envisions an application of these methods to other situations such as isolated singularities of complete intersections and to non-isolated singularities, including the development of a Picard-Lefschetz theory for non-isolated singularities using stratified Morse theory and intersection homology theory.
