characteristic class

definition:

1. pullbacks of characteristic classes on universal bundle
2. axiom
3. topological obstruction theory-Cech cohomology

eg. Chern class
Chern-Weil homomorphism: $H^2(M,\mathbb{Z})\to H^2(M,\mathbb{R})$
intersection theory: $c_1$ can be viewed as pullback of Thom form via a zero section
The first Chern class is the curvature.