Groups have played a big role in knot theory. We show how subfactors (subalgebras of certain von Neumann algebras) lead to unitary representations of the braid groups and Thompson’s groups \({F}\) and \({T}\). All knots and links may be obtained from geometric constructions from these groups. And invariants of knots may be obtained as coefficients of these representations. We include an extended introduction to von Neumann algebras and subfactors.

中文翻译：

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结，组，子因子和物理

群体在打结理论中发挥了重要作用。我们展示了子因子（某些冯·诺伊曼代数的子代数）如何导致辫子群和汤普森群\（{F} \）和\（{T} \）的统一表示。所有的结和链节都可以从这些组的几何构造中获得。结的不变量可以作为这些表示的系数来获得。我们包括对冯·诺依曼代数和子因子的扩展介绍。