The polynomials on \(w_ 1,w_ 2\) and \(w_ 3\) in the universal Wu classes (Q1917226)

The cohomology ring \(H^*(BO;\mathbb{Z}_2)\) is the polynomial algebra \(\mathbb{Z}_2[w_1,w_2,\dots]\), where \(w_i\) is the \(i\)th universal Stiefel-Whitney class. The \(i\)th Wu class \(v_i\) is defined inductively by: \(v_0=w_0=1\) and \(v_i=w_i+\sum^i_{j=1} Sq^jv_{i-j}\) for \(i\geq 1\), where \(Sq^j\) is the Steenrod squaring operation. Let \(I_k\) denote the ideal of \(H^*(BO;\mathbb{Z}_2)\) generated by \(w_i\) for \(i\geq k\). The paper under review gives explicit polynomials for \(v_i\) in terms of the Stiefel-Whitney classes \(\text{mod }I_4\).