Stiefel-Whitney class

Okay kiddo, the Stiefel-Whitney class is like a special way of looking at something called a vector bundle. A vector bundle is kind of like a bunch of arrows that sit on each point of a shape, like a ball, and all the arrows point in the same direction.

Now, the Stiefel-Whitney class helps us understand how these arrows twist and turn around as we move from one point on the ball to another. It's like when we twist a rubber band, it starts to have a twisty shape.

The Stiefel-Whitney class can tell us how many times the arrows twist or turn in a certain way as we move around the ball. It's like counting how many times we twisted the rubber band.

This information is very useful because it helps us understand more about the shape of the object that we're looking at. It's kind of like using a map to navigate a new city. The Stiefel-Whitney class helps us navigate the twists and turns of the arrows on the shape.

So, in summary, the Stiefel-Whitney class is a special way of looking at how arrows twist and turn on a shape, which helps us understand more about the shape itself.