Some notes on the adams spectral sequence

Abstract

In the beginning of 1980's Cohen, R. proved thath0b(1k)=B(1,k)=B(1,k)⊗ζ₁ survives toE _∞ in the Adams spectral sequence. Later, Cohen, R. and Goerss, P. proved that is a permanent cycle. And they are represented by ζ _k ,ηj respectively. Here the author proved: Theorem 2: Let 2≤s≤p−1,j≥3, then β _s η _j ≠0. Theorem 3: For 2≤s≤p−1,k≥2, β _s ζ _k ≠0 in the stable homotopy groups of spheres.

As a remark, we get$\beta _s \beta _{p^k /p^k - 1} \ne 0$ in$Ext_{B P*BP}^{*,*} (BP*,BP*)$.