On the mapping class groups of $\mathbb{P}^1$-bundles over $\mathbb{P}^2$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909972603863040 |
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| author | Hu, TengLin |
| author_facet | Hu, TengLin |
| contents | In this article we compute the mapping class group of the total space $S(ξ)$ of the sphere bundle of a 3-dimensional real vector bundle $ξ$ over the complex projective plane $\mathbb{P}^2$ with $\langle p_1(ξ), [\mathbb{P}^2] \rangle =8n+5$. Examples of these manifolds include the Milnor hypersurface $M_1$ and its generalizations $M_k=\{(x,y)\in \mathbb{P}^2\times\mathbb{P}^2 \ | \ \sum x^k_iy_i=0\}$ with $k$ odd. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the mapping class groups of $\mathbb{P}^1$-bundles over $\mathbb{P}^2$ Hu, TengLin Geometric Topology Algebraic Topology In this article we compute the mapping class group of the total space $S(ξ)$ of the sphere bundle of a 3-dimensional real vector bundle $ξ$ over the complex projective plane $\mathbb{P}^2$ with $\langle p_1(ξ), [\mathbb{P}^2] \rangle =8n+5$. Examples of these manifolds include the Milnor hypersurface $M_1$ and its generalizations $M_k=\{(x,y)\in \mathbb{P}^2\times\mathbb{P}^2 \ | \ \sum x^k_iy_i=0\}$ with $k$ odd. |
| title | On the mapping class groups of $\mathbb{P}^1$-bundles over $\mathbb{P}^2$ |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2512.18590 |