关于 6、7 和 8 球体的 33 干同调群的扩展问题

arXiv - MATH - Algebraic Topology Pub Date : 2024-06-12 DOI:arxiv-2406.08621

Juxin Yang, Jie Wu

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引用次数: 0

摘要

本文探讨了同调群$\pi_{39}(S^{6})$、$\pi_{40}(S^{7})$和$\pi_{41}(S^{8})$在2处的扩展问题，这些问题四十五年来一直悬而未决。我们为不稳定同调群的确定性理论引入了一个工具，即$\mathcal{Z}$形托达括号，通过它我们能够解决这三个同调群的扩展问题。

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On the extension problems for the 33-stem homotopy groups of the 6-, 7- and 8-spheres

This paper tackles the extension problems for the homotopy groups $\pi_{39}(S^{6})$, $\pi_{40}(S^{7})$, and $\pi_{41}(S^{8})$ localized at 2, the puzzles having remained unsolved for forty-five years. We introduce a tool for the theory of determinations of unstable homotopy groups, namely, the $\mathcal{Z}$-shape Toda bracket, by which we are able to solve the extension problems with respect to these three homotopy groups.

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arXiv - MATH - Algebraic Topology

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