2022/05/02 by A. G. Kalugin, Kalugin, Alexey
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2205.00854
openalex publication_date 2022/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper, we study a relation between the cohomology of moduli stacks of smooth and proper curves \mathcal Mg,n and the cohomology of ribbon graph complexes. The main results of this work are proofs of T. Willwacher's conjecture and A. C\check\mathrm ald\check\mathrm araru's conjecture about the cohomology of the Bridgeland differential. We also discuss the relation to string topology and the Chan-Galatius-Payne theorem about the weight zero part of the compactly supported cohomology of \mathcal Mg,n.