Mathematical Sciences: 3-Manifold Invariants from Quantum Theory

首席研究员将继续研究 维滕定义的一个新的3-流形不变量（在 量子场论）和Reshetikhin和Turaev（在 量子群表示论（Representation Theory of Quantum Groups） 这些不变量在低维中心问题中的应用 维拓扑，包括与琼斯有关的问题 多项式和手术结，将进行研究。 的 将针对各种示例计算不变量，这些示例可以 希望能揭示周期性现象。 机器计算 在Macintosh IIci上使用Mathematica是可行的， 进行。

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.