Abstract:

In this article, by the algebraic method, the author proves the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres $\pi_rS$, which is represented by 0 ≠\widetilde{\gamma}_{s+3}h_nh_m\in {\rm Ex}t_A^{s+5,\ t}(Z_p, Z_p)$ in the Adams spectral sequence, where r=q(p^m+pⁿ+(s+3)p²+(s+2)p+(s+1))-5}, t=p^mq+pⁿq+(s+3)p²q+(s+2)pq+(s+1)q+s, p≥7, m≥n+2>5, 0≤s