_1g_0的收敛性

The Convergence of _1g_0

球面稳定同伦群的研究是同伦论中的一个重要课题,Smith-Toda谱V(n)的同伦群与球谱S的同伦群有极其紧密的联系.主要利用May谱序列证明珓g0在Adams谱序列中是永久循环且不是dr边缘,从而收敛到πp2q+3pq+2q-5(V(1))中的非零元,其中n=1,2,p≥11,q=2(p-1).

In homotopy theory,it is one of the important problems to determine the stable homotopy theory of a sphere,the homotopy group of Smith-Toda spectrumV（n）is in close tie with that of sphere spectrumS.In this paper,by using the May’s spectral sequence,we show that 1g0,in the Adams’ spectral sequence,is a permanent cycle and not a dr-boundary,and thus,it converges to a nontrivial element in πp2q＋3pq＋2q-5（V（1））where n=1,2,p≥11,q=2（p-1）.