Stiefel-Whitney w_i(E) ∈ H^i(B,Z/2); Chern c_i(E) ∈ H^{2i}(B,Z); Pontryagin. Obstruct triviality of vector-bundles. Splitting principle. Foundation of differential-topology.
Stiefel-Whitney w_i(E) ∈ H^i(B,Z/2); Chern c_i(E) ∈ H^{2i}(B,Z); Pontryagin. Obstruct triviality of vector-bundles. Splitting principle. Foundation of differential-topology.