Discrete Morse theory
Okay kiddo, so Discrete Morse Theory is a way to study and understand shapes called simplicial complexes. Remember when we learned about shapes like circles, squares, and triangles? Well simplicial complexes are shapes made up of smaller shapes called simplices.
The way we use Discrete Morse Theory is by looking at how these simplices are connected to each other in the shape. Sometimes there can be too many connections, making it hard to understand the shape. But, with Discrete Morse Theory we can simplify it!
We do this by looking for special points called critical points. A critical point is a point where the shape changes from going up to going down. Think of it like climbing a hill, when you reach the top that's a critical point.
We then remove any connections that are not important, connecting the simplices in a simpler way. This way we can understand the shape better and see its structure.
So, Discrete Morse Theory is like finding the easiest way to understand a complicated shape by looking for special points called critical points and simplifying the connections between simplices.
The way we use Discrete Morse Theory is by looking at how these simplices are connected to each other in the shape. Sometimes there can be too many connections, making it hard to understand the shape. But, with Discrete Morse Theory we can simplify it!
We do this by looking for special points called critical points. A critical point is a point where the shape changes from going up to going down. Think of it like climbing a hill, when you reach the top that's a critical point.
We then remove any connections that are not important, connecting the simplices in a simpler way. This way we can understand the shape better and see its structure.
So, Discrete Morse Theory is like finding the easiest way to understand a complicated shape by looking for special points called critical points and simplifying the connections between simplices.