The Witten-Reshetikhin-Turaev Invariants of 3-Manifolds

The Witten-Reshetikhin-Turaev invariantsWitten-Reshetikhin-Turaev invariant are fascinating 3-manifold invariants3-manifoldinvariant with connections to physics. In fact, their existence was predicted by Edward WittenWitten, E. in his work on Chern-Simons gauge theory and topological quantum field theoryTopological Quantum Field Theory. The invariants also have close connections to skein theory. In this lecture, we focus on W. B. Raymond Lickorish’sLickorish, W. B. R. Kauffman bracketKauffman bracketpolynomial skein theoretic approach to the invariants. In the last section of this lecture, we introduce a skein module described by Justin Roberts that incorporates the Jones-Wenzl idempotentsJones-Wenzl idempotentidempotent and has close connections to the (2 + 1)-TQFT and WRT invariants.