Reshetikhin–Turaev invariant

The reshetikhin-turaev invariant is a way to help us understand knots and links. Imagine you have a string that you tie into a knot or a bunch of knots, this is a knot or a link. The reshetikhin-turaev invariant helps us know if two knots or links are the same or different.

We have to use some special math to make this work. We use something called a group, which is like a club where we can only do certain things. We also use something called a representation, which is like a picture of the group that helps us understand it better.

Now, we take the string that is knotted up and put it in a special machine that has a big formula inside. This formula can tell us a special number that is different for every knot or link. We call this number the reshetikhin-turaev invariant.

This number can help us know if two knots or links are the same or different. Similar to how your friends can tell you apart by your hair or clothes, the different knots and links have different reshetikhin-turaev invariants that make them unique.

So, the reshetikhin-turaev invariant is like a secret code that helps us understand knots and links, and figure out if they are the same or different.