Tame topology

Imagine you have a small piece of paper, and you want to fold it into different shapes. You might fold it into a simple square, or you could get more creative and make something like a paper crane. This is kind of like what mathematicians do with shapes called "manifolds."

Manifolds are like pieces of paper, but with many more dimensions. They can be twisted and turned in different ways, just like a piece of paper can be folded. One thing mathematicians like to do is figure out what shapes a manifold can be "deformed" into, without cutting or tearing it.

This is where "tame topology" comes in. Topology is the branch of math that studies shapes and their properties. When we say "tame," we mean that the manifolds can be deformed in a very controlled way. Think of it like folding the piece of paper into precise, neat shapes instead of crumpling it up into a ball.

Why do mathematicians care about tame topology? It helps us understand the structure of shapes in a precise way, and can give us information about how things behave in the real world. For example, if we're studying the shape of a protein molecule, we might use ideas from tame topology to understand how the molecule can twist and fold in specific ways.

So, in short, tame topology is a fancy way of studying the way shapes can be deformed in specific, controlled ways. It helps us understand the structure of complex objects and can give us insights into how things behave in the real world.