On the mapping class groups of ℙ¹-bundles over ℙ²

2025/12/21 by TengLin Hu, Hu, TengLin
Mathematics · #Algebraic Geometry and Number Theory #Bundle #Class (philosophy) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Group (periodic table) #Hypersurface #Manifold (fluid mechanics) #Plane (geometry) #Projective space #Space (punctuation) #math.AT #math.GT

paper · pdf · open access · doi:10.48550/arxiv.2512.18590

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/12/21 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

Abstract

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 ℙ² with ⟨ p₁(ξ), [ℙ²] ⟩ =8n+5. Examples of these manifolds include the Milnor hypersurface M₁ and its generalizations M_k=\(x,y)∈ ℙ²×ℙ² | ∑ x^k_iy_i=0\ with k odd.

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