UC Berkeley

An important milestone of the theory of knot invariants is the Reshetikhin-Turaev functor introduced in [RT]. This construction could generate tangle invariants from quantum groups. Later, Kashaev and Reshetikhin generalizes this construction [KR1] based on the idea of the holonomy braiding, the braiding defined for C-colored diagrams. The purpose of this work is to have some discussion of this construction. There are three parts in this thesis: first the full description of the construction is provided. Then in the second part, some examples computed via Mathematica are shown. And some properties and theorems are given in the end.