Complex-oriented cohomology theory

Okay kiddo, so you know that when we talk about shapes and spaces in math, we can sometimes use math tools to help us understand them better? One of those math tools is cohomology theory.

Cohomology theory helps us look at a space and figure out what kind of holes or twists or turns it has. It's like a map that tells us what's going on inside the space.

Now, sometimes the spaces we want to study are really complicated. They have lots of twists and turns and loops and holes all interacting with each other. That's where complex-oriented cohomology theory comes in.

You see, sometimes we can understand these complicated spaces if we look at them through a special pair of glasses (math tools, really) called the complex numbers. The complex numbers are like regular numbers, but they also include imaginary numbers.

When we use complex-oriented cohomology theory, we're looking at the cohomology of a space through these special glasses. It can help us see patterns and symmetries that we might have missed otherwise.

So, think of cohomology theory like a map, and complex-oriented cohomology theory like a special pair of glasses we can wear to see the complicated map more clearly. Does that make sense?