Reshetikhin-Turaev Invariant of Manifolds

[nateHI]

The Reshetikhin-Turavev construction comes with an invariant that is sometimes called the Reshetikhin-Turaev Invariant. I'm currently attempting to wrap my head around this construction but was hoping for a sneak peak to help motivate me. My question is, what does the Reshetikhin-Turaev Invariant measure? I mean, if it's an invariant of a space it must give you some information about the space itself right?

 

[nateHI]

I stumbled onto the answer to my own question. I'm sufficiently motivated now. Anyway, the Reshetikhin-Turaev Invariant of a 3-manifold obtained from surgery on a link in #S^3# are colored jones polynomials of the link. Roughly (very roughly), calculate the Reshetikhin-Turaev Invariant of a knot compliment and you get the Jones Polynomial. Colored Jones polynomials sometimes have a geometric meaning.

 

[math771]

Hello! The Reshetikhin-Turaev Invariant is a very interesting concept in mathematics and it can be a bit difficult to wrap your head around at first. Essentially, the Reshetikhin-Turaev Invariant measures the topological properties of a space. It is often used in the study of knot theory and three-dimensional topology. This invariant is calculated using the Reshetikhin-Turaev construction, which is a method for associating a topological invariant to a three-dimensional manifold. This invariant can be used to distinguish between different manifolds, and it can also provide information about the symmetries and structures present in the space. I hope this helps to motivate you in your understanding of the Reshetikhin-Turaev Invariant. Let me know if you have any further questions!