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

2025/08/20 by Zhu, Zhongjian, Pan, Jianzhong
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.14341

Abstract

In this paper, we classify the homotopy types of the total spaces of S^2k-1-bundles (or fibrations) over S^2k for 2≤ k≤ 6 by listing the attaching map of the top cell of these as CW-complexes. The method is using the new necessary and sufficient conditions we gave in our previous work to determine whether a CW complex has the homotopy type of total space of these sphere bundles.

Citations

• Homotopy types of S^2k-1-bundles over S^2k
• The unstable homotopy groups of 2-cell complexes
• A classification of S³-bundles over S⁴

Related

• Homotopy types of S^2k-1-bundles over S^2k
• On the Classification of S³-Bundles over ℂP²
• A classification of S³-bundles over S⁴
• Lusternik-Schnirelmann category of a sphere-bundle over a sphere
• On Complexes Equivalent to \mathbbS³-bundles over \mathbbS⁴