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The cohomology of the full directed graph complex. (English) Zbl 07210933
Summary: In his seminal paper “Formality conjecture”, M. Kontsevich introduced a graph complex \(\mathsf{GC}_{1ve}\) 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 \(\mathsf{GC}_{1ve}\). 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.
MSC:
53D55 Deformation quantization, star products
53D17 Poisson manifolds; Poisson groupoids and algebroids
57Q45 Knots and links in high dimensions (PL-topology) (MSC2010)
18M60 Operads (general)
05C10 Planar graphs; geometric and topological aspects of graph theory
05E15 Combinatorial aspects of groups and algebras (MSC2010)
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