The ${\mathbb S}_n$-equivariant Euler characteristic of the moduli space of graphs
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866908627113082880 |
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| author | Borinsky, Michael Vermaseren, Jos |
| author_facet | Borinsky, Michael Vermaseren, Jos |
| contents | We prove a formula for the ${\mathbb S}_n$-equivariant Euler characteristic of the moduli space of graphs $\mathcal{MG}_{g,n}$. Moreover, we prove that the rational ${\mathbb S}_n$-invariant cohomology of $\mathcal{MG}_{g,n}$ stabilizes for large $n$. That means, if $n \geq g \geq 2$, then there are isomorphisms $H^k(\mathcal{MG}_{g,n};\mathbb{Q})^{{\mathbb S}_n} \rightarrow H^k(\mathcal{MG}_{g,n+1};\mathbb{Q})^{{\mathbb S}_{n+1}}$ for all $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_15598 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The ${\mathbb S}_n$-equivariant Euler characteristic of the moduli space of graphs Borinsky, Michael Vermaseren, Jos Algebraic Topology High Energy Physics - Theory Mathematical Physics Group Theory 58D29, 18G85, 14D22 (Primary) 05E18, 14T99, 20F28, 20F65, 20J06 (Secondary) We prove a formula for the ${\mathbb S}_n$-equivariant Euler characteristic of the moduli space of graphs $\mathcal{MG}_{g,n}$. Moreover, we prove that the rational ${\mathbb S}_n$-invariant cohomology of $\mathcal{MG}_{g,n}$ stabilizes for large $n$. That means, if $n \geq g \geq 2$, then there are isomorphisms $H^k(\mathcal{MG}_{g,n};\mathbb{Q})^{{\mathbb S}_n} \rightarrow H^k(\mathcal{MG}_{g,n+1};\mathbb{Q})^{{\mathbb S}_{n+1}}$ for all $k$. |
| title | The ${\mathbb S}_n$-equivariant Euler characteristic of the moduli space of graphs |
| topic | Algebraic Topology High Energy Physics - Theory Mathematical Physics Group Theory 58D29, 18G85, 14D22 (Primary) 05E18, 14T99, 20F28, 20F65, 20J06 (Secondary) |
| url | https://arxiv.org/abs/2306.15598 |