Loop Space Splittings of Sphere Bundles over Highly Connected Poincaré Complexes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866908928506331136 |
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| author | Shen, Wen |
| author_facet | Shen, Wen |
| contents | Let $m > n \ge 2$, and let $N$ be an $(n-1)$-connected $2n$-Poincaré complex. In this paper, we establish sufficient conditions under which the loop space of the total space $M$ of the sphere bundle $S^{m-1} \to M \to N$ (associated to a rank-$m$ real vector bundle over $N$) splits as a product of the loop spaces of $N$ and $S^{m-1}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00406 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Loop Space Splittings of Sphere Bundles over Highly Connected Poincaré Complexes Shen, Wen Algebraic Topology Let $m > n \ge 2$, and let $N$ be an $(n-1)$-connected $2n$-Poincaré complex. In this paper, we establish sufficient conditions under which the loop space of the total space $M$ of the sphere bundle $S^{m-1} \to M \to N$ (associated to a rank-$m$ real vector bundle over $N$) splits as a product of the loop spaces of $N$ and $S^{m-1}$. |
| title | Loop Space Splittings of Sphere Bundles over Highly Connected Poincaré Complexes |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2604.00406 |