Oriented hairy graphs and moduli spaces of curves
Abstract
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 Mg,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 Mg,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.
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