在线阅读 --自然科学版 2020年5期《Adams谱序列上的一个非平凡积b0g0ãs+4(4)
Adams谱序列上的一个非平凡积b0g0ãs+4(4)--[在线阅读]
蔡玉梅, 王玉玉
天津师范大学 数学科学学院, 天津 300387
起止页码: 369--374页
DOI: 10.13763/j.cnki.jhebnu.nse.2020.05.001
摘要
p≥11,0≤s<p-4时,以May谱序列为工具,证明了在Adams谱序列的E2项中,乘积b0g0ãs+4(4)∈ExtAs+8,tsZpZp)是非平凡的,其中ts)=q[(s+4)p3+(s+3)p2+(s+4)p+(s+3)]+s.

A Nontrivial Product b0g0ãs+4(4) in the Adams Spectral Sequence
CAI Yumei, WANG Yuyu
College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
Abstract:
In this paper,the May spectral sequence is used to prove the non-triviality of product b0g0ãs+4(4)∈ExtAs+8,t(s)(Zp,Zp) in the E2-term of the Adams spectral sequence,where p≥11,0≤s<p,t(s)=q[(s+4)p3+(s+3)p2+(s+4)p+(s+3)]+s.

收稿日期: 2019-10-20
基金项目: 国家自然科学基金(11301386);天津市自然科学基金(19JCYBJC30300)

参考文献:
[1]ADAMS J.Stable Homotopy and Generalised Homology[M].Chicago:University of Chicago Press,1974.
[2]RAVENEL D.Complex Cobordism and Stable Homotopy Groups of Spheres[M].Orlando:Academic Press,1986.
[3]LIULEVICIUS A.The Factorization of Cyclic Reduced Powers by Secondary Cohomology Operations[J].Mem Amer Math Soc,1962,42:1-112.doi:10.2307/70759
[4]AIKAWA T.3-dimensional Cohomology of the Mod p Steenrod Algebra[J].Math Scand,1980,47(1):91-115.doi:10.7146/math.scand.a-11876
[5]WANG X J,ZHENG Q B.The Convergence of nsh0hk[J].Sci China Ser A,1998,41(6):622-628.doi:10.1007/BF02876232
[6]LIU X G,ZHAO H.On a Product in the Classical Adams Spectral Sequence[J].Pro Amer Math Soc,2009,137(7):2489-2496.doi:10.1090/S0002-9939-09-09809-8
[7]LIU X G,WANG H.On a Cohomology of the Mod p Steenrod Algebra[J].Proc Japan Acad,2009,85(9):143-148.doi:10.3792/pjaa.85.143
[8]ZHONG L N,WANG Y Y.Detection of a Nontrivial Product in the Stable Homotopy Groups of Spheres[J].Algebr Geom Topol,2013,13(5):3009-3029.doi:10.2140/agt.2013.13.3009
[9]YU H B,KOU Y L,ZHAO H.Detection of a Nontrivial Element in the Stable Homotopy Groups of Spheres[J].Bull Iranian Math Soc,2015,41(1):65-85.