Symplectic filling
Okay kiddo, let's imagine you have a toy box that's shaped like a cube. You can put all your favorite toys in it and there's still some room left for more toys. Now let's pretend that you have a bigger box shaped like a sphere, but it's currently empty. You want to fill the big box with all the toys from the small cube box.
This is kind of like what happens in math when we talk about symplectic filling.
In math, many shapes have what's called a "symplectic structure." This is just a fancy way of saying that they have a certain kind of mathematical property that makes them interesting to study.
A shape that has a symplectic structure can be thought of as a toy box, but instead of toys, it contains other mathematical objects called "symplectic forms." These forms are like rules that explain how points in the shape can move around, kind of like how you move your toys around inside your toy box.
When we talk about symplectic filling, we're basically asking whether or not we can take one symplectic shape (like the small cube toy box) and "fill" a bigger symplectic shape (like the empty sphere toy box) with its symplectic forms.
If we can fill the shape completely without any empty spaces, we say the small shape is "symplectic fillable." If there are some empty spaces left after we try to fill the big shape, we say the small shape is "not symplectic fillable."
So in the end, symplectic filling is just a way for mathematicians to study how different symplectic shapes relate to each other, and see if they can be filled up with other symplectic shapes.
This is kind of like what happens in math when we talk about symplectic filling.
In math, many shapes have what's called a "symplectic structure." This is just a fancy way of saying that they have a certain kind of mathematical property that makes them interesting to study.
A shape that has a symplectic structure can be thought of as a toy box, but instead of toys, it contains other mathematical objects called "symplectic forms." These forms are like rules that explain how points in the shape can move around, kind of like how you move your toys around inside your toy box.
When we talk about symplectic filling, we're basically asking whether or not we can take one symplectic shape (like the small cube toy box) and "fill" a bigger symplectic shape (like the empty sphere toy box) with its symplectic forms.
If we can fill the shape completely without any empty spaces, we say the small shape is "symplectic fillable." If there are some empty spaces left after we try to fill the big shape, we say the small shape is "not symplectic fillable."
So in the end, symplectic filling is just a way for mathematicians to study how different symplectic shapes relate to each other, and see if they can be filled up with other symplectic shapes.