Stiefel–Whitney class

《Class Field Theory》 · 第 217 页 · Section 6.3

For each real vector bundle \(\xi\) over \(M\), the Stiefel–Whitney classes \(w_i(\xi)\in H^i(M;\mathbb F_2)\) satisfy \(w_0=1\), vanish above the rank, are natural under pullback, and obey \(w(\xi\oplus\eta)=w(\xi)w(\eta)\).