Categorical enumerative invariants of the ground field
| Autor: | Tu, Junwu |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | For an $S^1$-framed modular operad $P$, we introduce its "Feynman compactification" denoted by $FP$ which is a modular operad. Let $\{\mathbb{M}^{\sf fr}(g,n)\}_{(g,n)}$ be the $S^1$-framed modular operad defined using moduli spaces of smooth curves with framings along punctures. We prove that the homology operad of $F\mathbb{M}^{\sf fr}$ is isomorphic to $H_*(\overline{M})$, the homology operad of the Deligne-Mumford operad. Using this isomorphism, we obtain an explicit formula of the fundamental class of $[\overline{M}_{g,n}/S_n]$ in terms of Sen-Zwiebach's string vertices. As an immediate application, under mild assumptions, we prove that Costello's categorical enumerative invariants of the ground field match with the Gromov-Witten invariants of a point. Comment: 40 pages, 5 figures; the comparison in the semi-simple case needs considerably more work and is removed in this version; revised and some parts rewritten |
| Databáze: | arXiv |
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