Kirby calculus

Kirby calculus is like playing with toy blocks, but with shapes that are more complex than basic squares and rectangles. Think of it like building different kinds of castles and houses with blocks that are shaped like animals, people, and other fun things.

In math, Kirby calculus is a way to understand and study 4-dimensional spaces. These spaces are like the toy blocks, but instead of building with physical blocks, we use mathematical concepts and tools called diffeomorphisms.

Diffeomorphisms are like instructions that tell us how to change the shape of our block-like shapes without stretching or tearing them. It's like when we take a toy block and rotate it, flip it over, or move it around to make a different shape, but without breaking it.

Using diffeomorphisms, we can take different shapes and find ways to connect them together that preserve their overall structure. This is like taking our toy blocks and figuring out how to snap them together in different ways to make new and interesting shapes.

The end result of Kirby calculus is a way of understanding and visualizing complex 4-dimensional spaces in terms of simpler pieces that we can put together like blocks. This can help us solve difficult problems and gain new insights into the mysterious world of higher dimensions.