Rank (differential topology)
Okay kiddo, so imagine you have a map, like a treasure map. And on this map, there are different roads and paths that lead you to the treasure. The rank of a map is like how many paths you have to choose from on the map.
Now, imagine you have two maps, but they're a little different. One map has more paths to choose from than the other map. The map with more paths has a higher rank than the other one.
In differential topology, we look at maps that take us from one place to another, but instead of roads and paths on a treasure map, we have something called "manifolds". Manifolds are like shapes that we can stretch and bend, but they still keep their original shape.
So, when we talk about the rank of a map in differential topology, we're really talking about how many directions or paths we have to choose from when we move between two manifolds. And just like with treasure maps, maps with more paths have a higher rank than maps with fewer paths.
Why do we care about rank in differential topology? Well, it helps us to understand how manifolds are related to each other and to find ways to move between them. It's kind of like having a map that shows you all the shortcuts and alternate routes to your treasure. The higher the rank, the more options you have to get there!
Now, imagine you have two maps, but they're a little different. One map has more paths to choose from than the other map. The map with more paths has a higher rank than the other one.
In differential topology, we look at maps that take us from one place to another, but instead of roads and paths on a treasure map, we have something called "manifolds". Manifolds are like shapes that we can stretch and bend, but they still keep their original shape.
So, when we talk about the rank of a map in differential topology, we're really talking about how many directions or paths we have to choose from when we move between two manifolds. And just like with treasure maps, maps with more paths have a higher rank than maps with fewer paths.
Why do we care about rank in differential topology? Well, it helps us to understand how manifolds are related to each other and to find ways to move between them. It's kind of like having a map that shows you all the shortcuts and alternate routes to your treasure. The higher the rank, the more options you have to get there!