Mathematical Sciences: Geometry and Topology of 3-Dimensional Manifolds

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This project is concerned with problems in 3-dimensional manifold theory through the application and extension of differential geometric methods. It aims to explore the classification of non-Haken 3-manifolds and their diffeomorphisms, Heegaard splittings of 3-manifolds and universal coverings of 3- manifolds. The plan is to use the theory of minimal surfaces and of flows and evolution equations to study these problems. Three- dimensional manifolds are very natural objects of study, inasmuch as the space we live in (ignoring time) has three dimensions, but a surprising amount remains to be learned about them.