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arXiv · 2002.10734

The Deligne-Mumford operad as a trivialization of the circle action

Alexandru Oancea·Dmitry Vaintrob
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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.

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Alexandru Oancea, Dmitry Vaintrob. 2020-02-25. The Deligne-Mumford operad as a trivialization of the circle action. https://doi.org/10.2140/agt.2026.26.1229

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