Let $T_{operatorname{poly}}(mathbb{R}^d)$ denote the space of skew-symmetric polyvector fields on $mathbb{R}^d$, turned into a graded Lie algebra by means of the Schouten bracket. Our aim is to explore the cohomology of this Lie algebra, with coefficients in the adjoint representation, arising from cochains defined by linear combination of aerial Kontsevich graphs. We prove that this cohomology is localized at the space of graphs without any isolated vertex, any “hand” or any “foot”. As an application, we explicitly compute the cohomology of the “ascending graphs” quotient complex.
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机译：令$ T _ { operatorname {poly}}（ mathbb {R} ^ d）$表示$ mathbb {R} ^ d $上的斜对称多矢量字段的空间，该空间通过肖滕支架。我们的目的是探索这种李代数的同调性，其伴随表示中的系数是由空中Kontsevich图的线性组合定义的共链产生的。我们证明了这种同调性位于图的空间中，没有任何孤立的顶点，任何“手”或“脚”。作为应用程序，我们显式计算“升图”商群的同调。
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