球面稳定同伦群中的一族新元素及h_0b_1~2在π_*V(1)中的收敛性  

A NEW FAMILY ELEMENTS IN THE STABLE HOMOTOPY GROUP OF SPHERES AND THE CONVERGENCE OF h_0~2_1 IN π_*V(1)

作　　者：王健波[1] 胡林敏[2] 

机构地区：[1]内蒙古大学数学系,呼和浩特010021 [2]燕山大学数学系,河北秦皇岛066004

出　　处：《数学年刊（A辑）》2005年第3期375-384,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10171049)资助的项目.

摘　　要：对连通有限型谱x,y,存在着Adams谱序列(ASS){Es,tr,dr}满足(1)dr:Es,tr→Es+r,t+r-1r 是谱序列的微分,(2)Es,t2≌Exts,tA(H*(X),H*(Y)),(3)并且收敛到[∑t-sY,X]p.当X是球谱S, Moore谱M,Toda-Smith谱V(1)时,(πt-sX)p分别为S,M,v(1)的稳定同伦群.本文通过Adams 谱序列,发现了球谱S的稳定同伦群中的一族非零元素γth0b21及Toda-Smith谱V(1)的稳定同伦群中的非零元素h0b21.在利用Adams谱序列求解同伦群的过程中,需要计算有关Exts,tA(H*X,H*Y) 的结果.利用谱的上纤维序列导出的Ext群的正合序列和May谱序列,得出Exts,tA(H*X,H*Y)的某些结果.本文令p≥7为奇素数,q=2(p-1).For connected finite type spectra X, Y. there exists Adams spectral sequence (ASS) (Exr,t,dr) such that (1) dr : Es,tr→Es+r,t+r-1 r is the differential, (2)Es,t2≌Exts,tA(H*(X),H*(Y)), (3) converges to [∑t-sY,X]p. When X is sphere spectrum S, Moore spectum M, Toda-Smith spectrum V(1) respectively, (πt-sX)p is respectively the stable homotopy group of S, M, V(1). This paper detects a new family nonzero elements γth0b21 of the stable homotopy groups of sphere and a nonzero element h0b21 of Toda-Smith spectrum V(1) by using of the ASS. The authors need some results on Ext group by using of the Ext group exact sequences induced by cofibrations of spectrum and by using of May spectral sequence. In this paper, p≥7, which is an odd prime number, and q =2p-1.

关 键 词：稳定同伦群 球谱 TODA-SMITH谱 ADAMS谱序列 MAY谱序列 

分 类 号：O189.23[理学—数学]