Complexes equivalent to S^2k-1-fibrations over S^2k

2025/08/19 by Zhongjian Zhu, Zhu, Zhongjian, Jianzhong Pan +1 · 1 citation
Computer Science · Mathematics · #Algebraic Topology (math.AT) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2508.13800

openalex publication_date 2025/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, necessary and sufficient conditions are obtained for the attaching map f of the top cell of a CW complex to have the homotopy type of the total space of S^2k-1-fibration over S^2k for any k≥ 2. As an application, the order of any attaching map of the top cell of the total space of an S^2k-1-fibration over S^2k is determined and when k≠ 2,4, the homotopy types of the total spaces of S^2k-1-fibrations over S^2k are classified by the stable homotopy classes of the attaching maps.

Citations

• A classification of S³-bundles over S⁴

Cited by

• Homotopy classification of S^2k-1-bundles over S^2k

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