Cobordism theory

Okay, imagine you have two puzzles. One is a big red puzzle, and the other is a smaller blue puzzle. You notice that they have the same shapes of puzzle pieces, but the red puzzle has more of them. So, you start to wonder if you can turn the blue puzzle into the red puzzle by adding extra puzzle pieces.

This is kind of like what cobordism theory is all about. Instead of puzzles, we're talking about certain shapes called manifolds. Some manifolds are bigger and have more dimensions, like a beach ball, while others are smaller and flatter, like a frisbee. They also come in different shapes and sizes, just like puzzle pieces.

Cobordism theory is interested in studying when two different manifolds can be turned into each other by adding or taking away puzzle pieces, or more technically, by gluing them together or cutting them apart. This process is called cobordism.

Just like our red and blue puzzles, there are ways to cobord certain manifolds that have the same shapes and dimensions, but different sizes. Scientists use cobordism theory to study which manifolds can be cobordant to each other, meaning that they can be turned into each other by adding or removing puzzle pieces.

The study of cobordism theory can tell us a lot about the shapes and sizes of manifolds, and can help us understand how they are related to each other.