Cohomology operation

Imagine we have a bunch of shapes, like circles, squares, and triangles. We want to assign a number to each shape that tells us something about it. But we can't just use normal numbers, like 1, 2, 3, because we want these numbers to work with something called cohomology.

Cohomology is like a way to measure holes or twists in shapes. If we have a shape with a big hole in the middle, its cohomology number will be different from a shape with a small hole, even if the shapes are the same size.

Now, the cohomology operation is a way to change these numbers. It's kind of like a math machine that takes in a shape and spits out a new number for that shape. But it doesn't just give us any number - it gives us a number that's related to the shape's cohomology.

So, if we have a circle with a cohomology number of 2, and we use the cohomology operation on it, we might get a new number, like 5. But this new number still tells us something about the circle's cohomology - it might mean there's a twist in the circle.

Basically, the cohomology operation is a tool that helps us understand the "twists and turns" of shapes. It takes in a shape's cohomology number and gives us a new number that's related to that cohomology.