Mathematical Sciences: Some Problems in Geometric Topology

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Ferry plans to study problems in several areas of geometric topology. The problems are concerned with constructing closed manifolds containing a given open manifold as a codimension-zero submanifold, characterizing open subsets of Euclidean space, studying which open manifolds may be deformed into each other via Hurewicz fibrations, and finding when a map with acyclic homotopy fiber is homotopic to a map with acyclic point-inverses. Understanding 3-manifolds is particularly valuable, since they are the natural setting for studying many questions about our physical habitat.