2020/02/25 by Alexandru Oancea, Oancea, Alexandru, Dmitry Vaintrob +1 · 1 citation
Mathematics · #14D22 #18D50 #18G30 #58D29 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2002.10734
openalex publication_date 2020/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the tree-like Deligne-Mumford operad is a homotopical model for the trivialization of the circle in the higher-genus framed little discs operad. Our proof is based on a geometric argument involving nodal annuli. We use as a model for the higher-genus framed little discs an operad of Riemann surfaces with analytically parametrized boundary. We develop the formalism of topological moduli problems as a framework to accommodate the orbifold nature of the Deligne-Mumford operad.