Homology operations for gravity algebras
Abstract
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 $H_{*}^{\Sigma_{n}}(\mathcal{M}_{0,n+1};\mathbb{F}_{p})$ and $H_{*}^{\Sigma_{n}}(\mathcal{M}_{0,n+1};\mathbb{F}_{p}(\pm1))$ for any $n\in\mathbb{N}$ and any prime p, where $\mathbb{F}_{p}(\pm1)$ denotes the sign representation of the symmetric group $\Sigma_{n}$. 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 $(\mathcal{M}_{0,n+1})_{\Sigma_{n}}$ is a model for the classifying space for $B_{n}/Z(B_{n})$, the quotient of the braid group $B_{n}$ by its center.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Advanced Topics in Algebra
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Homology Homotopy and Applications
- Publisher
- International Press of Boston
- Volume
- 28
- Issue
- 2
- Pages
- 193–221
- Publication date
- 1 January 2026
- Language
- EN