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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2504.18507 |
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Table des matières:
- 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.