The Deligne-Mumford operad as a trivialization of the circle action
- Resource Type
- Working Paper
- Authors
- Oancea, Alexandru; Vaintrob, Dmitry
- Source
- Subject
- Mathematics - Algebraic Topology
Mathematics - K-Theory and Homology
Mathematics - Symplectic Geometry
55P48, 53D37, 14J33, 14J33
- Language
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 Riemann surfaces with analytically parametrized boundary as a model for higher-genus framed little discs.
Comment: V2: 70 pages. We rewrote the appendices in the language of topological moduli problems and Segal operads. We split the proof of the main theorem in two parts for readability: genus zero, respectively arbitrary genus. Added details in the proofs and corrected some inconsistencies