Toroidal embedding

Okay kiddo, imagine you have a toy called a hula hoop. You know how you can slide your arms and body through the hula hoop to make it go around you? That's basically what toroidal embedding is, but with something called a manifold.

A manifold is like a squishy 3D shape that's made up of lots of tiny pieces that fit together perfectly. Now imagine wrapping that shape into a big circle, like a hula hoop. But instead of it being a flat circle, it's a curved circle that goes all the way around and connects to itself. This is called a torus.

When we take a manifold and wrap it around a torus in this way, that's called toroidal embedding. It's like we're putting the manifold inside the hula hoop, and then bending the hula hoop into a torus shape so that the manifold wraps around it like a cocoon.

Why would we want to do this? Well, sometimes it helps us understand the shape of a manifold better if we can see how it fits inside a torus. It's also useful for studying things like knots and curves in the manifold.

So there you have it, toroidal embedding is like putting a squishy shape into a hula hoop that's been bent into a circle shape so that the shape wraps around it like a cocoon.