May谱序列的一些注记

数学物理学报

May谱序列的一些注记

刘秀贵

南开大学数学科学学院;核心数学与组合数学教育部重点实验室天津 300071

收稿日期:2005-03-29 修回日期:2006-03-22 出版日期:2007-10-25 发布日期:2007-10-25
通讯作者: 刘秀贵
基金资助:
国家自然科学基金(10501045)和南开大学人事处科研启动基金 (J02017)资助

Some Notes on the May Spectral Sequence

Liu Xiugui

School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071

Received:2005-03-29 Revised:2006-03-22 Online:2007-10-25 Published:2007-10-25
Contact: Liu Xiugui

摘要/Abstract

摘要： 令 p>5 是素数, A 表示模 p Steenrod代数, S 表示球谱的 p 局部化. 首先给出了有关May谱序列的一些重要定理, 然后作为应用, 利用May谱序列和Adams谱序列发觉了一族新的非零的球面稳定元素. 该新元素族次数为2(p-1)(pⁿ+sp²+sp+s)-7,在Adams谱序列中由 b_n-1g0γ_s∈ Ext_A^s+4,﹡( Z_pZ_p)所表示, 其中n≥4, 3≤s

该文的主要定理是文献[1]中的定理I的一个推广.

关键词: 球面稳定同伦群, Adams谱序列, Toda-Smith谱, May谱序列

Abstract: Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p , where p>5 is an arbitrary odd prime. In this paper, some important propositions on the May spectral sequence are first given, and then a new nontrivial family of homotopy elements is detected in the stable homotopy groups of spheres by the May spectral sequence and the Adams spectral sequence. The new one is of degree p(p-1)(pⁿ+sp²+sp+s)-7) and is represented by b_n-1g0γ_sin the E₂^s+4,﹡-term of the Adams spectral sequence, where n 4≥ and 3≤ s<p-2. The main theorem obtained in this paper is an obvious generalization of Theorem I in [1].

Key words: Stable homotopy groups of spheres, Adams spectral sequence, Toda-Smith spectra, May spectral sequence

中图分类号:

55Q45

刘秀贵. May谱序列的一些注记[J]. 数学物理学报, 2007, 27(5): 802-810.

Liu Xiugui. Some Notes on the May Spectral Sequence[J]. Acta mathematica scientia,Series A, 2007, 27(5): 802-810.

[1]	钟立楠, 刘秀贵. Adams 谱序列上的非平凡乘积b₀k₀δ_s₊₄[J]. 数学物理学报, 2014, 34(2): 274-282.
[2]	刘秀贵. 球面稳定同伦元素α₁β₁β_s的非平凡性[J]. 数学物理学报, 2007, 27(2): 208-214.