The Cohomology of the Full Directed Graph Complex

被引：2

作者：

Dolgushev, Vasily A. ^{[1
]}

Rogers, Christopher L. ^{[2
]}

机构：

[1] Temple Univ, Dept Math, Wachman Hall Rm 638 1805 N Broad St, Philadelphia, PA 19122 USA

[2] Univ Nevada, Dept Math & Stat, Reno 1664 N Virginia St, Reno, NV 89557 USA

来源：

ALGEBRAS AND REPRESENTATION THEORY | 2020年 / 23卷 / 03期

关键词：

Graph complexes; Formality theorems; DIFFERENTIALS; OPERADS;

D O I：

10.1007/s10468-019-09875-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：917 / 961

页数：45

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