Manifolds are the main object of study in topology. They are the spaces which are locally homeomorphic to euclidean spaces. Often a manifold E comes equipped with a map p:E--B onto another manifold which is locally a product projection. Such a map is called a bundle projection. The controlled topology of E is the study of certain classical topics in the topology of manifolds on which restrictions are placed reflecting the bundle structure on E. These restrictions usually take the form of metric control measured in B. This project is concerned with the study of controlled homotopy equivalences, controlled simple homotopy theory, and controlled pseudo-isotopies. These technical investigations are important because manifolds are ubiquitous in topology, geometry, analysis, even mathematical physics.
