The unstable homotopy groups of 2-cell complexes

2024/10/27 by Zhongjian Zhu, Zhu, Zhongjian · 1 citation
Biochemistry, Genetics and Molecular Biology · Medicine · #Algebraic Topology (math.AT) #Chronic Lymphocytic Leukemia Research #FOS: Mathematics #Glycosylation and Glycoproteins Research #Monoclonal and Polyclonal Antibodies Research

paper · pdf · doi:10.48550/arxiv.2410.20416

openalex publication_date 2024/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we develop the new method, initiated by B. Gray (1972), to compute the unstable homotopy groups of the mapping cone, especially for 2-cell complex X=S^m∪_α eⁿ. By Gray's work mentioned above or the traditional method given by I.M.James (1957) which were widely used in previous related work to compute π_i(X), the dimension i≤ 2n+m-4. By our method, we can compute π_i(X) for i>2n+m-4. We use this different technique to generalize J.Wu's work, at Mem. of AMS, on homotopy groups of mod 2 Moore spaces to higher dimensional homotopy groups of mod 2^r Moore spaces Pⁿ(2^r) for all r≥ 1. This practice shows that the technique given here is a new general method to compute the unstable homotopy groups of CW complexes with higher dimension.

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• Homotopy classification of S^2k-1-bundles over S^2k

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