论文标题
图电位和拓扑量子场理论
Graph potentials and topological quantum field theories
论文作者
论文摘要
我们介绍了图形电势，这些势是与（有色）三价图相关的laurent多项式。我们表明，图势的偶然类型仅取决于彩色图的同喻类型，并使用它来定义拓扑量子场理论。最近，Kontsevich-Odesskii以乘法核的名义独立引入了类似的结构。我们通过提供有效的计算方法来计算其分区功能来结束论文。这是系列中的第一篇论文，我们对其他部分中图电位的应用进行了调查。
We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. We show that the birational type of the graph potential only depends on the homotopy type of the colored graph, and use this to define a topological quantum field theory. A similar construction was recently introduced independently by Kontsevich--Odesskii under the name of multiplicative kernels. We end our paper by giving an efficient computational method to compute its partition function. This is the first paper in a series, and we give a survey of the applications of graph potentials in the other parts.
