Canonical class

A canonical class is like a special sticker that we put on certain shapes to make them look extra pretty.

Imagine you have a piece of paper with a bunch of shapes on it, like circles, squares, and triangles. Some shapes are easy to draw, like squares, and some are harder, like circles. But if we put a special sticker on certain shapes, we can make them look just as easy to draw as squares, even if they were originally harder.

In math, shapes are called manifolds, and we use a special tool called differential geometry to study them. Some manifolds are easy to work with, and some are harder. We use a canonical class to label certain manifolds as "easier" to work with, even if they were originally more complicated.

Just like a sticker on a shape can make it look nicer, a canonical class can help us understand a manifold better by giving us a standard way of looking at it. And just like some shapes don't need stickers to look nice, some manifolds don't have a canonical class because they are already easy to work with.