The Deligne-Mumford operad as a trivialization of the circle action
arXiv:2002.10734 · doi:10.2140/agt.2026.26.1229
Abstract
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.
V3: 74 pages, 9 figures. Expanded the Introduction, added context and background. Provided details for Propositions A.19 and A.28 in the Appendix. Various other minor modifications. Final version to be published in Algebraic and Geometric Topology