Homology operations for gravity algebras
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914128432463872 |
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| author | Rossi, Tommaso |
| author_facet | Rossi, Tommaso |
| contents | Let $\mathcal{M}_{0,n+1}$ be the moduli space of genus zero Riemann surfaces with $n+1$ marked points. In this paper we compute $H_*^{Σ_n}(\mathcal{M}_{0,n+1};\mathbb{F}_p)$ and $H_*^{Σ_n}(\mathcal{M}_{0,n+1};\mathbb{F}_p(\pm 1))$ for any $n\in\mathbb{N}$ and any prime $p$, where $\mathbb{F}_p(\pm 1)$ denotes the sign representation of the symmetric group $Σ_n$. The interest in these homology groups is twofold: on the one hand classes in these equivariant homology groups parametrize homology operations for gravity algebras. On the other hand the homotopy quotient $(\mathcal{M}_{0,n+1})_{Σ_n}$ is a model for the classifying space for $B_n/Z(B_n)$, the quotient of the braid group $B_n$ by its center. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10639 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homology operations for gravity algebras Rossi, Tommaso Algebraic Topology Algebraic Geometry Group Theory Let $\mathcal{M}_{0,n+1}$ be the moduli space of genus zero Riemann surfaces with $n+1$ marked points. In this paper we compute $H_*^{Σ_n}(\mathcal{M}_{0,n+1};\mathbb{F}_p)$ and $H_*^{Σ_n}(\mathcal{M}_{0,n+1};\mathbb{F}_p(\pm 1))$ for any $n\in\mathbb{N}$ and any prime $p$, where $\mathbb{F}_p(\pm 1)$ denotes the sign representation of the symmetric group $Σ_n$. The interest in these homology groups is twofold: on the one hand classes in these equivariant homology groups parametrize homology operations for gravity algebras. On the other hand the homotopy quotient $(\mathcal{M}_{0,n+1})_{Σ_n}$ is a model for the classifying space for $B_n/Z(B_n)$, the quotient of the braid group $B_n$ by its center. |
| title | Homology operations for gravity algebras |
| topic | Algebraic Topology Algebraic Geometry Group Theory |
| url | https://arxiv.org/abs/2404.10639 |