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

Fuente: arXiv
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Main Authors: Yang, Juxin, Lei, Fengchun, Li, Jingyan, Wu, Jie
Format: Preprint
Published: 2025
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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
id 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