Homotopy classification of $S^{2k-1}$-bundles over $S^{2k}$
Homotopy classification of $S^{2k-1}$-bundles over $S^{2k}$
In this paper, we classify the homotopy types of the total spaces of $S^{2k-1}$-bundles (or fibrations) over $S^{2k}$ for $2\leq k\leq 6$ 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.
Zhongjian Zhu、Jianzhong Pan
数学
Zhongjian Zhu,Jianzhong Pan.Homotopy classification of $S^{2k-1}$-bundles over $S^{2k}$[EB/OL].(2025-08-20)[2025-09-02].https://arxiv.org/abs/2508.14341.点此复制
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