Link invariants from classical Chern-Simons theory

Taking as the starting point a perturbative study of the classical equations of motion of the non-Abelian Chern-Simons theory with nondynamical sources, we obtain analytical expressions for link invariants. In order to present these expressions in a manifestly diffeomorphism-invariant form, we introduce a set of differential forms associated with submanifolds in $R^3$ that are metric independent, and that allow us to consider the link invariants as a kind of surface-dependent diffeomorphism invariant that presents a certain Abelian gauge symmetry.