Mathematical Sciences: Low-dimensional Manifolds and Knot Theory

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Gordon will continue to investigate problems in the topology of low-dimensional manifolds, particularly those related to knot theory. Two topics which will receive attention are the Dehn surgery construction on knots and links, and Heegaard splittings. Both of these are relevant to many fundamental questions concerning the structure of 3-dimensional manifolds. In fact investigations of knots have begun to find applications in organic chemistry, in addition to their connections with other parts of mathematics, particularly representation theory of operator algebras.