Topological aspects of non-abelian Chern-Simons theory

We introduce the non-abelian Chern-Simons functional in 3 dimensions and the corresponding partition function. Via the Faddeev-Popov gauge fixing procedure and the stationary phase approximation we evaluate the 1-loop contribution to the partition function. In order to investigate the metric dependence of the resulting expression, we make use of some mathematical results by Albert Schwarz and the Atiyah-Patodi-Singer index theorem. The final result shows that the partition function depends on the metric in a simple, controllable way. We also elaborate on the possibility of removing such dependence by adopting a different choice of regularization scheme.