Mapping class group

The mapping class group is like a big club for shapes. Imagine you have a bunch of different shapes like circles, squares, and triangles. Now, you can do things to these shapes like flipping them, twisting them, and bending them. It's kind of like when you play with Play-Doh and you can squish it and mold it into new shapes.

The mapping class group is interested in studying all the different ways you can move these shapes around while still keeping their basic shape. They call these movements "mappings." The group is like a group of friends who study these mappings and try to understand how they work.

In math terms, the mapping class group is a group that consists of all the possible ways you can transform a shape while still keeping its basic structure. The group is interested in understanding the properties of these mappings and how they relate to each other.

So, in short, the mapping class group is a group of people who study the different ways you can move shapes around while still keeping their basic structure. They try to understand how these movements work and how they relate to each other in math terms.