论文标题
曲线的定向毛茸茸的图形和模量空间
Oriented hairy graphs and moduli spaces of curves
论文作者
论文摘要
我们讨论由带有外腿的定向无环图形成的图形复合物。该复合物特别是带有色带图复合物的地图计算点$ \ mathcal m_ {g，n} $的模量空间的（紧凑支持的）共同体，从而扩大了Merkulov-Willwacher的较早结果。此外，根据chan-galatius-payne，它是$ \ Mathcal {M} _ {M} _ {M} _ {M} _ {M} _ {M} $的毛状图0计算重量0的一部分。因此，我们可以自然地连接木 - 加拉图斯 - 佩恩（Chan-Galatius-Payne）和默克洛夫·威尔瓦切（Merkulov-Willwacher）和色带图复合物，并获得相当令人满意的图片，说明所有碎片和各种图形复合物如何将其融合在一起，至少以零为零。
We discuss a graph complex formed by directed acyclic graphs with external legs. This complex comes in particular with a map to the ribbon graph complex computing the (compactly supported) cohomology of the moduli space of points $\mathcal M_{g,n}$, extending an earlier result of Merkulov-Willwacher. It is furthermore quasi-isomorphic to the hairy graph complex computing the weight 0 part of the compactly supported cohomology of $\mathcal{M}_{g,n}$ according to Chan-Galatius-Payne. Hence we can naturally connect the works Chan-Galatius-Payne and of Merkulov-Willwacher and the ribbon graph complex and obtain a fairly satisfying picture of how all the pieces and various graph complexes fit together, at least in weight zero.
