In his seminal paper “Formality conjecture”, M. Kontsevich introduced a graph complex GC_1ve closely connected with the problem of constructing a formality quasi-isomorphism for Hochschild cochains. In this paper, we express the cohomology of the full directed graph complex dfGC explicitly in terms of the cohomology of GC_1ve. Applications of our results include a recent work by the first author which completely characterizes homotopy classes of formality quasi-isomorphisms for Hochschild cochains in the stable setting.

中文翻译：

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有向图复合体的同调

M. Kontsevich在他的开创性论文“形式猜想”中，引入了图复杂GC _{1 v e，}它与为Hochschild共链构造形式准同构问题密切相关。在本文中，我们根据GC _{1 v e}的同调性明确表达了完全有向图复杂dfGC的同调性。我们的结果的应用包括第一作者的最新工作，该工作在稳定的环境中完全刻画了Hochschild共链形式形式准同构的同伦类。