38. Characteristic Classes
We define general characteristic classes and state and prove the Chern-Weil Theorem. We then introduce the Pontryagin classes of a vector bundle.
As an application, we show that $ \mathbb{C}P^2$ does not embed in $ \mathbb{R}^5$.
Of course this only scratches the surface of what is possible with characteristic classes! If you are interested, I recommend taking a course in Algebraic Topology.
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