The Deligne-Mumford operad as a trivialization of the circle action
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866917461237956608 |
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| author | Oancea, Alexandru Vaintrob, Dmitry |
| author_facet | Oancea, Alexandru Vaintrob, Dmitry |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_10734 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Deligne-Mumford operad as a trivialization of the circle action Oancea, Alexandru Vaintrob, Dmitry Algebraic Topology K-Theory and Homology Symplectic Geometry 14D22, 18D50, 18G30, 58D29 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. |
| title | The Deligne-Mumford operad as a trivialization of the circle action |
| topic | Algebraic Topology K-Theory and Homology Symplectic Geometry 14D22, 18D50, 18G30, 58D29 |
| url | https://arxiv.org/abs/2002.10734 |