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Oriented hairy graphs and moduli spaces of curves

Assar Andersson, Thomas Willwacher, Marko Zivkovic

1/5/20 Published in : arXiv:2005.00439

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.

Entire article

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  • Field Theory
  • Geometry, Topology and Physics

S-duality and correlation functions at large R-charge

Lecture notes on the Gaussian Free Field

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