球面稳定同伦元素α_1β_1β_s的非平凡性

Non-triviality of an Elementα_1β_1β_s in the Stable Homotopy of Spheres

决定球面稳定同伦群是同伦论中的核心问题之一,是非常重要的．该文证明:球面稳定同伦元素α1β1βs是一个阶为p的非平凡元素,其中p≥5是任意奇素数,1≤s<p．

To determine the stable homotopy groups of spheres π＊S is one of the central problems in homotopy theory. In this paper, it is proved that, for p ≥ 5 to be an arbitrary odd prime number and 1 ≤ s 〈 p, the homotopy element а1β1βs is nontrivial and of order p in the stable homotopy groups of spheres π＊S.