A pull back theorem in the Adams spectral sequence

Abstract

This paper proves that, for any generator x e ExtAs,tq (Zp, Zp), if (1L ⋀ i)*φ*(x) e ExtAs+1,tq+2q (H*L ⋀ M,Zp) is a permanent cycle in the Adams spectral sequence (ASS), then h0x e ExtAs+1,tq+q (Zp, Zp) also is a permenent cycle in the ASS. As an application, the paper obtains that h0hnhm ∈ \( Ext_A^{3,p^n q + p^m q + q} (Z_p ,Z_p ) \) is a permanent cycle in the ASS and it converges to elements of order p in the stable homotopy groups of spheres \( \pi _{p^n q + p^m q + q - 3} S \), where p ≥ 5 is a prime, s ≤ 4, n ≥ m+2 ≥ 4 and M is the Moore spectrum.