The secondary differentials on the third line of the Adams spectral sequence
As the title indicates, the author computes the Adams differential \(d_2\) on the \(E_2\)-term Ex\(^3=\) Ext\(_{A_*}^3({\mathbb Z}/p,{\mathbb Z}/p)\) of the Adams spectral sequence converging to the stable homotopy groups of spheres at a prime greater than three. He decomposes the \(E_2\)-term into three summands \(T\), \(C\) and \(N\), and shows that \(T\) is the image of the Thom map \(\Phi: H^3BP_*\to\) Ex\(^3\) from the \(E_2\)-term of the Adams-Novikov spectral sequence to that of the Adams spectral sequence, and the elements of \(C\) correspond to elements in \(H^sBP_*\) for \(s<3\). This implies that \(d_2\) acts trivially on \(T\oplus C\). On every generator of the other summand \(N\), the differential \(d_2\) is computed to be non-zero. The computation is based on the relation \(d_2(h_{i+1})=a_0b_i\) and the relations on the matrix Massey products.
scientific article; zbMATH DE number 5522066
scientific article