Suspension Splitting and Cohomotopy Sets of Simply Connected $7$-manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911107770220544 |
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| author | Huang, Ruizhi Li, Pengcheng |
| author_facet | Huang, Ruizhi Li, Pengcheng |
| contents | Let $M$ be a closed simply connected $7$-manifold. In this paper we establish homotopy decompositions of the reduced suspension space $ΣM$ into a wedge sum of simpler spaces when localized at a set of primes. These decompositions are applied to study the cohomotopy sets $π^k(M)$ and the $p$-local cohomotopy sets $π^4(M;\mathbb{Z}_{(p)})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_13145 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Suspension Splitting and Cohomotopy Sets of Simply Connected $7$-manifolds Huang, Ruizhi Li, Pengcheng Algebraic Topology Geometric Topology Let $M$ be a closed simply connected $7$-manifold. In this paper we establish homotopy decompositions of the reduced suspension space $ΣM$ into a wedge sum of simpler spaces when localized at a set of primes. These decompositions are applied to study the cohomotopy sets $π^k(M)$ and the $p$-local cohomotopy sets $π^4(M;\mathbb{Z}_{(p)})$. |
| title | Suspension Splitting and Cohomotopy Sets of Simply Connected $7$-manifolds |
| topic | Algebraic Topology Geometric Topology |
| url | https://arxiv.org/abs/2208.13145 |