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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.18507 |
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| _version_ | 1866908337814110208 |
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| author | Tokuda, Tomoki |
| author_facet | Tokuda, Tomoki |
| contents | In this paper, we compute the singular cohomology groups $H^*(C_2(M);\mathbb{F}_2)$ of the ordered 2-configuration space $C_2(M)$ as $Σ_2$-representations. Using the result, we determine the mod 2 cohomology of the unordered 2-configuration space $B_2(M)$ as a $H^*(\mathbb{R}P^{\infty};\mathbb{F}_2)$-module. As a corollary of our computation, we see that the Stiefel--Whitney height of $M$ is $2$ or $3$ when $M$ is orientable or not, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18507 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mod 2 cohomology of 2-configuration space of a closed surface and Stiefel--Whitney class Tokuda, Tomoki Algebraic Topology Representation Theory In this paper, we compute the singular cohomology groups $H^*(C_2(M);\mathbb{F}_2)$ of the ordered 2-configuration space $C_2(M)$ as $Σ_2$-representations. Using the result, we determine the mod 2 cohomology of the unordered 2-configuration space $B_2(M)$ as a $H^*(\mathbb{R}P^{\infty};\mathbb{F}_2)$-module. As a corollary of our computation, we see that the Stiefel--Whitney height of $M$ is $2$ or $3$ when $M$ is orientable or not, respectively. |
| title | Mod 2 cohomology of 2-configuration space of a closed surface and Stiefel--Whitney class |
| topic | Algebraic Topology Representation Theory |
| url | https://arxiv.org/abs/2504.18507 |