Combinatorial topology

Alright little buddy, let me explain it to you in a way that makes sense. Combinatorial topology is like having a box full of different shaped Lego pieces that you can put together to make something cool like a spaceship or a castle.

But instead of Legos, we have a bunch of shapes called "simplices" that we can put together to make different things. These simplices are like the Lego bricks in that we can stack them and attach them to each other in different ways.

Now imagine we have a bunch of these simplices and we want to arrange them in such a way that they make a solid object, like a cube. By putting these simplices together, we can create something called a "simplicial complex", which is like a collection of these simplices that fit together to create a bigger object. The simplicial complex can be used to study the properties of the object that we have made, such as how many corners, edges, and faces it has.

But we don't just use simplices to make objects - we can also use them to study abstract shapes or structures like graphs, networks, or even DNA molecules. By using combinatorial topology to break down and analyze these objects, we can better understand their properties and relationships.

So there you have it, little buddy - combinatorial topology is like playing with Legos, but instead of making physical objects, we use shapes called simplices to create simplicial complexes that help us understand abstract objects and structures.