Mathematical Sciences: Presidential Young Investigator Award

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This Presidential Young Investigator Award will enhance support for John E. Luecke's research in Dehn Surgery on Links, a topic in the topology of three-dimensional manifolds. A link in a 3-dimensional manifold, M, is a collection of circles embedded in M. A knot is a link of one component. The work this year will have two aspects: (1) understanding when a non-hyperbolic manifold results from Dehn surgery on a knot with hyperbolic complement, (2) generalizing results about Dehn surgery on knots to results about Dehn surgery on links with more than one component. Manifolds are natural objects of study, being spaces which are locally but in general not globally like Euclidean space. The case of three dimensions is the lowest dimension for which the closed manifolds have not been fully classified. Knots and links are also natural objects, about which it is surprising how basic are some of the questions still unanswered.