Cohomotopy Sets of $(n-1)$-connected $(2n+2)$-manifolds for small $n$
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866908350938087424 |
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| author | Li, Pengcheng Pan, Jianzhong Wu, Jie |
| author_facet | Li, Pengcheng Pan, Jianzhong Wu, Jie |
| contents | Let $M$ be a closed orientable $(n-1)$-connected $(2n+2)$-manifold, $n\geq 2$. In this paper we combine the Postnikov tower of spheres and the homotopy decomposition of the reduced suspension space $ΣM$ to investigate the cohomotopy sets $π^\ast(M)$ for $n=2,3,4$, under the assumption that $M$ has $2$-torsion-free homology. All cohomotopy sets $π^i(M)$ of such manifolds $M$ are characterized except $π^4(M)$ for $n=3,4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cohomotopy Sets of $(n-1)$-connected $(2n+2)$-manifolds for small $n$ Li, Pengcheng Pan, Jianzhong Wu, Jie Algebraic Topology Geometric Topology 55Q55, 57N65, 55P15, 55P40 Let $M$ be a closed orientable $(n-1)$-connected $(2n+2)$-manifold, $n\geq 2$. In this paper we combine the Postnikov tower of spheres and the homotopy decomposition of the reduced suspension space $ΣM$ to investigate the cohomotopy sets $π^\ast(M)$ for $n=2,3,4$, under the assumption that $M$ has $2$-torsion-free homology. All cohomotopy sets $π^i(M)$ of such manifolds $M$ are characterized except $π^4(M)$ for $n=3,4$. |
| title | Cohomotopy Sets of $(n-1)$-connected $(2n+2)$-manifolds for small $n$ |
| topic | Algebraic Topology Geometric Topology 55Q55, 57N65, 55P15, 55P40 |
| url | https://arxiv.org/abs/2410.16055 |