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arXiv · 1711.04701

The cohomology of the full directed graph complex

Vasily A. Dolgushev·Christopher L. Rogers
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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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Vasily A. Dolgushev, Christopher L. Rogers. 2017-11-13. The cohomology of the full directed graph complex. https://arxiv.org/abs/1711.04701

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