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arXiv · 2509.21444

A "Periodicity" Phenomenon of the Attaching Map of the Suspended Two-Cell Complex

Juxin Yang·Fengchun Lei·Jingyan Li·Jie Wu
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Abstract

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 $\pi_{18} (\Sigma^{3}\mathbb{C}P^{2})$, a homotopy group outside the metastable range.

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Juxin Yang, Fengchun Lei, Jingyan Li, Jie Wu. 2025-09-25. A "Periodicity" Phenomenon of the Attaching Map of the Suspended Two-Cell Complex. https://arxiv.org/abs/2509.21444

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