Mathematical Sciences: Low Dimensional Topology

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Freedman has recently been concerned with applications of topology to other areas of mathematics, including geometry, ideal MHD, and signal processing, as well as continuing his program in four-dimensional manifold theory. Thurston's geometrization conjecture is the most interesting problem in the latter area, and the analytic tools for studying it, such as Hamilton's equation, may now be available. With the addition of a time dimension, the world we live in is a four-dimensional manifold, which makes it that much more intriguing that dimension four is where various anomalies in manifold theory occur. Freedman was one of the prime movers in discovering these. For example, in all other dimensions there is only one differentiable structure on n-space, i.e. one way of doing calculus, but in dimension four this is known not to be the case.