The cohomology of the full directed graph complex

2017/11/13 by Dolgushev, Vasily A., Rogers, Christopher L.
#FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1711.04701

Abstract

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 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.

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