Stratified Morse theory
Okay kiddo, let me try to explain stratified Morse theory to you in a way that you can understand!
Have you ever heard of a mountain? Imagine a big mountain with different layers or levels. Each level has different things on it, like trees, rocks, and rivers.
Stratified Morse theory is kinda like climbing this mountain and studying the different levels. It helps us understand how things change as we move from one level to the next.
Now, let's imagine that instead of a mountain, we're looking at a shape or a space. This shape might be made up of different levels, just like the mountain. We can use stratified Morse theory to understand how this shape changes as we move from one level to the next.
But how do we do this? Well, let me introduce you to a special tool called a Morse function. A Morse function is like a map that tells us how high or low different points on our shape are. By studying this map, we can see how things change as we move up or down the different levels.
For example, imagine our shape is a donut. The Morse function might tell us that the highest point on the donut is at the top center, and the lowest point is in the hole in the middle. As we move around the edge of the donut, things change, and we'll see different parts of the shape.
Stratified Morse theory helps us take this idea even further. By looking at how different parts of the shape are connected at different levels, we can see how the whole shape fits together.
So, that's stratified Morse theory in a nutshell! It's like climbing a mountain and studying the different layers, but with shapes instead of rocks and trees. And by using a Morse function, we can see how things change as we move up and down the different levels.
Have you ever heard of a mountain? Imagine a big mountain with different layers or levels. Each level has different things on it, like trees, rocks, and rivers.
Stratified Morse theory is kinda like climbing this mountain and studying the different levels. It helps us understand how things change as we move from one level to the next.
Now, let's imagine that instead of a mountain, we're looking at a shape or a space. This shape might be made up of different levels, just like the mountain. We can use stratified Morse theory to understand how this shape changes as we move from one level to the next.
But how do we do this? Well, let me introduce you to a special tool called a Morse function. A Morse function is like a map that tells us how high or low different points on our shape are. By studying this map, we can see how things change as we move up or down the different levels.
For example, imagine our shape is a donut. The Morse function might tell us that the highest point on the donut is at the top center, and the lowest point is in the hole in the middle. As we move around the edge of the donut, things change, and we'll see different parts of the shape.
Stratified Morse theory helps us take this idea even further. By looking at how different parts of the shape are connected at different levels, we can see how the whole shape fits together.
So, that's stratified Morse theory in a nutshell! It's like climbing a mountain and studying the different layers, but with shapes instead of rocks and trees. And by using a Morse function, we can see how things change as we move up and down the different levels.