Hyperbolic Dehn surgery
Okay kiddo, imagine you have a really long balloon. You can hold onto the two ends, but you can also twist and turn the balloon in different ways. This will create different shapes along the balloon.
Now, imagine that this balloon represents a three-dimensional shape called a hyperbolic manifold. It's really hard to imagine what this looks like, but it's sort of like a squishy blob with an infinite number of little hills and valleys on its surface.
Sometimes, we want to change the shape of this hyperbolic manifold by doing something called "surgery." This means that we take out a little chunk of it and put in a new, different-shaped piece instead to make it look different.
But not just any old piece will do! We have to choose a special shape for the piece we put in so that the new shape is still a hyperbolic manifold. If we don't choose the right shape, it could turn into something else entirely.
This kind of surgery is called "Dehn surgery," named after a mathematician named Max Dehn. And when we do this kind of surgery on a hyperbolic manifold, we call it "hyperbolic Dehn surgery."
It might sound complicated, but basically, it's like playing with a squishy balloon and pulling and poking it to make it look different, all while making sure it stays the same basic shape.
Now, imagine that this balloon represents a three-dimensional shape called a hyperbolic manifold. It's really hard to imagine what this looks like, but it's sort of like a squishy blob with an infinite number of little hills and valleys on its surface.
Sometimes, we want to change the shape of this hyperbolic manifold by doing something called "surgery." This means that we take out a little chunk of it and put in a new, different-shaped piece instead to make it look different.
But not just any old piece will do! We have to choose a special shape for the piece we put in so that the new shape is still a hyperbolic manifold. If we don't choose the right shape, it could turn into something else entirely.
This kind of surgery is called "Dehn surgery," named after a mathematician named Max Dehn. And when we do this kind of surgery on a hyperbolic manifold, we call it "hyperbolic Dehn surgery."
It might sound complicated, but basically, it's like playing with a squishy balloon and pulling and poking it to make it look different, all while making sure it stays the same basic shape.