Oriented hairy graphs and moduli spaces of curves

2020/05/01 by Assar Andersson, Thomas Willwacher, Andersson, Assar +3
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #FOS: Mathematics #Quantum Algebra (math.QA) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2005.00439

openalex publication_date 2020/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \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 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.

Citations

• Relative (non-)formality of the little cubes operads and the algebraic\n Cerf Lemma
• Differentials on Graph Complexes III - Deleting a Vertex
• The rational homotopy of mapping spaces of E_n operads
• Euler characteristics for spaces of string links and the modular envelope of L_∞
• Hairy graphs to ribbon graphs via a fixed source graph complex

Related

• Hairy graphs to ribbon graphs via a fixed source graph complex
• Weight 11 Compactly Supported Cohomology of Moduli Spaces of Curves in excess four
• Semistable Graph Homology
• Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves
• On the Caldararu and Willwacher conjectures