乘积元b_(0g0)■_s在Adams谱序列中的收敛性

The Convergence of Products b_(0g0)■_s in the Adams Spectral Sequence

决定球面稳定同伦群是同伦中的一个中心问题,同时也是非常困难的问题之一.Adams谱序列是其计算的最有效的工具.在本文,令p>5为素数,A表示模p的Steenrod代数.我们利用Adams谱序列和May谱序列证明了:在球面稳定同伦群π+S中,存在一族在Adams谱序列中由b0g0■s∈Ext_A^(s+4,sp^2q+(s+1)pq+sq+s-3)(Z_p,Z_p)所表示的新的非平凡元素,其中q=2(p-1), 3≤s<p.

To determine the stable homotopy groups of spheres is not only one of the central problems in homotopy theory, but also a very difficult problem. The Adams spectral sequence is the most successful tool in computing it. Let p 〉 5 be an arbitrary prime and A be the modp Steenrod algebra. In this paper, using the Adams spectral sequence and the May spectral sequence we prove the existence of a new family of nontrivial homotopy elements in the stable homotopy of spheres which is represented up to nozero scalar by bogoγs in the E2^s＋4,＊-term of the Adams spectral sequence, where 3 ≤ s 〈 p.