球面稳定同伦群中的一个新元素族$b_1g_0\tilde{\gamma}_s$

设$p\geq 7$素数,$A$为模$p$的Steenrod代数. 我们利用Adams谱序列证明了球面稳定同伦群$\pi_{\ast}S$中,存在由$b_1g_0\tilde{\gamma}_{s}\in Ext_A^{s+4,(s+1)p^2q+spq+sq+s-3}(Z_p,Z_p)$所表示的新的非平凡元素族,其中$q=2(p-1)$, $3\leq s

A New Family Represented By $b_1g_0\tilde{\gamma}_s$ In The Stable Homotopy Groups Of Spheres

Let $p\geq 7$ be an arbitrary prime and $A$ be the mod $p$ Steenrod algebra. In this paper, using the Adams spectral sequence we prove the existence of a new family of nontrivial homotopy elements in the stable homotopy of spheres which is represented by $b_1g_0\tilde{\gamma}_s$ in the $E_2^{s+4,\ast}$-term of the Adams spectral sequence, where $3\leq s