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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.14341 |
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| _version_ | 1866918449127620608 |
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| author | Zhu, Zhongjian Pan, Jianzhong |
| author_facet | Zhu, Zhongjian Pan, Jianzhong |
| contents | In this paper, we classify the homotopy types of the total spaces of $S^{2k-1}$-bundles (or fibrations) over $S^{2k}$ for $2\leq k\leq 6$. One of the two key new ingredients in the argument is the new necessary and sufficient conditions for a CW complex to be homotopy equivalent to the total space of a sphere bundle (fibration); the other is a formula relating the attaching map of the top cell of the total space and the characteristic map of a sphere bundle for $k=2,4$. When $k=4$, the classification results provide a negative answer to the conjecture in [6]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14341 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homotopy classification of $S^{2k-1}$-bundles over $S^{2k}$ Zhu, Zhongjian Pan, Jianzhong Algebraic Topology In this paper, we classify the homotopy types of the total spaces of $S^{2k-1}$-bundles (or fibrations) over $S^{2k}$ for $2\leq k\leq 6$. One of the two key new ingredients in the argument is the new necessary and sufficient conditions for a CW complex to be homotopy equivalent to the total space of a sphere bundle (fibration); the other is a formula relating the attaching map of the top cell of the total space and the characteristic map of a sphere bundle for $k=2,4$. When $k=4$, the classification results provide a negative answer to the conjecture in [6]. |
| title | Homotopy classification of $S^{2k-1}$-bundles over $S^{2k}$ |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2508.14341 |