On the mapping class groups of $\mathbb{P}^1$-bundles over $\mathbb{P}^2$

Fuente: arXiv
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Main Author: Hu, TengLin
Format: Preprint
Published: 2025
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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