经典 Adams谱序列E₂-项中的非平凡乘积

Non-Trivial Products in the E₂-Term of the Classical Adams Spectral Sequence

摘要: 经典Adams 谱序列是研究球面稳定同伦群π_*S的最基本工具，利用May 谱序列的相关理论对Adams谱序列的E₂-项进行研究，具体给出了$${\tilde{\delta }}_{s+4}{h}_0{h}_n\in Ex{t}_A^{s+7,tq+s}(Z_p,Z_p)$$在Adams 谱序列中的非平凡性，其中p ≥ 11，n ≥ 2， 0 ≤ s ≤ p−5， t = pⁿ+(s+4)p³ +(s+3)p² +(s+2)p+(s+2)， q = 2(p−1)。

Abstract: The classical Adams spectral sequence is the most fundamental tool for studying the stable homotopy groups of spheres π_*S. By using the relevant theories of the May spectral sequence, we study the E₂-term of the Adams spectral sequence, and specifically give the non-triviality of $${\tilde{\delta }}_{s+4}{h}_0{h}_n\in Ex{t}_A^{s+7,tq+s}(Z_p,Z_p)$$ in the Adams spectral sequence,where p ≥ 11，n ≥ 2， 0 ≤ s ≤ p−5， t = pⁿ+(s+4)p³ +(s+3)p² +(s+2)p+(s+2)， q = 2(p−1).