Fundamental group

The fundamental group is like a secret code that tells you how shapes are connected together. Imagine you have a rubber band and you can twist and turn it around to make different shapes. Some shapes can be stretched and squished into each other, but others can't. The fundamental group tells you if two shapes can be squished and stretched into each other.

To get the fundamental group, you have to think about paths. A path is just a line that goes from one side of the shape to the other side. You can imagine a little ant crawling along the path. If the ant can crawl along the path and end up back where it started, that means the shape has a loop. The loop is like a hole in the shape that the ant crawled around.

The fundamental group is like all the different ways you can make loops by crawling along the paths in the shape. Each loop is its own secret code. If two shapes have the same fundamental group, that means they can be squished and stretched into each other.

So the fundamental group is like a secret code that helps you understand how shapes can be connected. It's like a little puzzle that tells you if shapes are the same or different.