谱V(1)同伦群中一些元素的存在性  

The existence of some elements in the homotopy group of spectrum V(1)

作　　者：蔡玉梅 李园园 王玉玉[1] CAI Yumei;LI Yuanyuan;WANG Yuyu(College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China)

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《华中师范大学学报（自然科学版）》2022年第3期383-388,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11301386);天津市自然科学基金项目(19JCYBJC30300).

摘　　要：利用May谱序列以及一些代数和数论的方法,证明了当p≥7时,b_(1)h_(1),b_(1)g_(0)在Adams谱序列中是永久循环且不是d_(r)边缘,从而分别收敛到同伦群π_(*)V(1)中相应的非零元,其中V(1)是Toda-Smith谱.In this paper,by using the May spectral sequence and combined with the algebraic and number-theoretical methods,for p≥7,it is proved that both b_(1)h_(1) and b_(1)g_(0) are permanent cycles in the Adams spectral sequence and not d_(r) boundaries.The corresponding nonzero elements of the homotopy group π_(*)V(1)will be detected,where V(1)is Toda-Smith spectrum.

关 键 词：Ext群 ADAMS谱序列 MAY谱序列 TODA-SMITH谱 存在性 

分 类 号：O189.23[理学—数学]