Fibered manifold

A fibered manifold is like a special type of map. Imagine you have a map that shows you how to get from your house to your friend's house. Now imagine that in addition to showing you the roads and streets to take, the map also tells you what color car to look for when you get to your friend's house. That's kind of what a fibered manifold is like.

In math terms, a fibered manifold is a space that has a certain structure that allows us to talk about how it looks at different points. Like the map example, at each point on the fibered manifold, there is a special set of instructions that tells us how it "fibered" or "looks" at that point. These instructions might say "look for a small sphere" or "look for a circle that's growing bigger and bigger."

The cool thing about fibered manifolds is that we can use them to help us understand other spaces, like geometric objects or shapes. By studying how a fibered manifold looks at different points, we can learn more about the bigger space it represents.