Mathematical Sciences: 3-Manifold Invariants from Quantum Theory

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The principal investigator will continue his study of the new 3-manifold invariants defined by Witten (in the context of quantum field theory) and by Reshetikhin and Turaev (in the context of representation theory of quantum groups). Applications of these invariants to central problems in low dimensional topology, including questions related to the Jones polynomial and to surgery on knots, will be investigated. The invariants will be computed for a variety of examples, which can be expected to reveal periodicity phenomena. Machine computation using Mathematica on a Macintosh IIci is feasible and will be undertaken.