Computation of Topological Invariants for Plumbed 3-Manifolds in SU(2)_k Chern-Simons Theory

Topological quantum field theories (TQFTs) have been studied extensively in physics and mathematics due to their applications to condensed matter systems, knot theory, and low-dimensional topology. Topological invariants of these theories, such as the Witten-Reshetikhin-Turaev (WRT) and the Turaev-Viro invariants, are of great interest, as they encode a wealth of information about the properties of a given system. In this work, we present the physical and mathematical motivation for the WRT invariant, as well as explicit computations of the invariant for classes of plumbed 3-manifolds. Use of computer methods to simplify certain calculations is discussed, as well as the potential for future improvement of these methods.