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The Chern-Simons-form is a topological invariant, related to the curvature-form $F=dA + A \wedge A$ through the dynamics equation $$\frac{\delta S}{\delta A}= \frac{k}{2 \pi} F$$ with $k$ the level, or the topological charge of the theory.

The Chern-simons form is non-trivial only in odd dimension manifolds. In three-dimension, the Chern-Simons form reads $$ S = \frac{k}{4 \pi} \int \text{Tr}\left[ A\wedge dA+\dfrac{2}{3}A\wedge A\wedge A\right] $$
for instance.

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