Categorical enumerative invariants of the ground field
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866914402895134720 |
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| author | Tu, Junwu |
| author_facet | Tu, Junwu |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_01383 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Categorical enumerative invariants of the ground field Tu, Junwu Symplectic Geometry Algebraic Geometry Algebraic Topology Quantum Algebra 53D45, 14N35, 57K20 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. |
| title | Categorical enumerative invariants of the ground field |
| topic | Symplectic Geometry Algebraic Geometry Algebraic Topology Quantum Algebra 53D45, 14N35, 57K20 |
| url | https://arxiv.org/abs/2103.01383 |