We review the gauge and ghost cyle graph complexes as defined by Kreimer, Sars and van Suijlekom in "Quantization of gauge fields, graph polynomials and graph homology" and compute their cohomology. These complexes are generated by labelings on the edges or cycles of graphs and the differentials act by exchanging these labels. We show that both cases are instances of a more general construction of double complexes associated to graphs. Furthermore, we describe a universal model for these kind of complexes which allows to treat all of them in a unified way.

中文翻译：

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规范论中标记图的复形

我们回顾了 Kreimer、Sars 和 van Suijlekom 在“规范场、图多项式和图同调的量化”中定义的规范和鬼环图复合体，并计算它们的上同调。这些复合体是由图的边或环上的标签生成的，而差异通过交换这些标签而起作用。我们表明，这两种情况都是与图相关的双复合体的更一般构造的实例。此外，我们为这些类型的复合体描述了一个通用模型，它允许以统一的方式处理所有这些复合体。