A "Periodicity" Phenomenon of the Attaching Map of the Suspended Two-Cell Complex
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917435478638592 |
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| author | Yang, Juxin Lei, Fengchun Li, Jingyan Wu, Jie |
| author_facet | Yang, Juxin Lei, Fengchun Li, Jingyan Wu, Jie |
| contents | In this paper, we determine the 3-cell skeleton of $F$, where $F$ is the homotopy fiber of the canonical pinch map from a suspension of a simply-connected 2-cell complex onto a sphere. The main result is stated $p$-locally: for $p=2$, and for $p\geq5$ under an additional assumption. The proof is based on Selick-Wu's $\mathrm{A}^{\mathrm{min}}$-theory and the machinery of the Eilenberg-Moore spectral sequence. As an application, we compute the 2-primary component of $π_{18} (Σ^{3}\mathbb{C}P^{2})$, a homotopy group outside the metastable range. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_21444 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A "Periodicity" Phenomenon of the Attaching Map of the Suspended Two-Cell Complex Yang, Juxin Lei, Fengchun Li, Jingyan Wu, Jie Algebraic Topology In this paper, we determine the 3-cell skeleton of $F$, where $F$ is the homotopy fiber of the canonical pinch map from a suspension of a simply-connected 2-cell complex onto a sphere. The main result is stated $p$-locally: for $p=2$, and for $p\geq5$ under an additional assumption. The proof is based on Selick-Wu's $\mathrm{A}^{\mathrm{min}}$-theory and the machinery of the Eilenberg-Moore spectral sequence. As an application, we compute the 2-primary component of $π_{18} (Σ^{3}\mathbb{C}P^{2})$, a homotopy group outside the metastable range. |
| title | A "Periodicity" Phenomenon of the Attaching Map of the Suspended Two-Cell Complex |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2509.21444 |