球面稳定同伦群中的周期性元素

确定球面稳定同伦群中的非平凡元素，特别是球面稳定同伦群中的第二周期性元素仍然是稳定同伦中的一个重要问题，比如Kervaire不变量1问题的解决就是通过确定Adams谱序列中某个元素的不存在性而得以解决的。而确定Adams谱序列中的元素hohn是否收敛是确定第二周期性元素的关键。本项目主要研究的第一个课题是hohn的收敛性。.另外一方面确定ao相关元素的收敛性是一种全新的发现球面稳定同伦中非平凡元素的方法，目前只发现了一对ao相关元素是收敛的。现在项目组成员发现有许多组ao相关元素,研究他们的收敛性是本项目的第二个研究课题。

To detect non-trivial homotopy classes in the stable homotopy groups of spheres especially to detect the secondary periodic family elements is one of the most important problem in stable homotopy theory. For example, the Kervaire invariant 1 problem was solved by determine a special element in the Adams spectral sequence does not exist. The key point to determine the secondray periodic family elements is to detect the convergence of hohn in the Adams spectral sequence. One aim of this research project is to determine some hohn does not exist.. On the other hand, to determine the convergenve of ao related element in the Adams spectral sequence is a new methord to detect non-trivial homotopy elements in stable homotopy groups. By now only one pair ao related elements are detected to be survive. Lately one member of this research project found many ao related elements by computing the Adams differential. The second aim of this project is to determine the convergince of these ao related elements.