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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2508.13800 |
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| _version_ | 1866914468274896896 |
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| author | Zhu, Zhongjian Pan, Jianzhong |
| author_facet | Zhu, Zhongjian Pan, Jianzhong |
| contents | 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 $k\geq 2$. 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 $k\ne 2,4$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13800 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complexes equivalent to $S^{2k-1}$-fibrations over $S^{2k}$ Zhu, Zhongjian Pan, Jianzhong Algebraic Topology 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 $k\geq 2$. 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 $k\ne 2,4$, 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. |
| title | Complexes equivalent to $S^{2k-1}$-fibrations over $S^{2k}$ |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2508.13800 |