Mod 2 representation of the symmetric group of order 2 over cohomology groups of 2-configuration space of torus
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910335143772160 |
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| author | Tokuda, Tomoki |
| author_facet | Tokuda, Tomoki |
| contents | In this article, we compute the mod 2 representarion of the symmetric group of order 2 over the singular cohomology groups of orderd 2-configuration space $C_{2}(T^{d})$ of the $d$-torus $T^{d}$ for $d\geq 1$. As applications of the computation, we determine the Stiefel-Whitney height of $C_{2}(T^{d})$ for any $d$, and determine $\mathbb{F}_{2}[Σ_{2}]$-module structure of the cohomology groups of the unordered 2-configuration space of the $d$-torus for $d=2,3$ using the Serre spectral sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_11277 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mod 2 representation of the symmetric group of order 2 over cohomology groups of 2-configuration space of torus Tokuda, Tomoki Algebraic Topology Representation Theory In this article, we compute the mod 2 representarion of the symmetric group of order 2 over the singular cohomology groups of orderd 2-configuration space $C_{2}(T^{d})$ of the $d$-torus $T^{d}$ for $d\geq 1$. As applications of the computation, we determine the Stiefel-Whitney height of $C_{2}(T^{d})$ for any $d$, and determine $\mathbb{F}_{2}[Σ_{2}]$-module structure of the cohomology groups of the unordered 2-configuration space of the $d$-torus for $d=2,3$ using the Serre spectral sequence. |
| title | Mod 2 representation of the symmetric group of order 2 over cohomology groups of 2-configuration space of torus |
| topic | Algebraic Topology Representation Theory |
| url | https://arxiv.org/abs/2402.11277 |