= Gauge change of the Chern-Simons three-form
For an anti-Hermitian $SU(N)$ <connection one-form>, normalize the <Chern-Simons three-form> by $1/(8\pi^2)$ and use $A^g=g^{-1}Ag+g^{-1}dg$. Its change is $-d\operatorname{Tr}(dg\,g^{-1}\wedge A)/(8\pi^2)-\operatorname{Tr}(g^{-1}dg)^3/(24\pi^2)$. On a closed three-manifold the first term integrates to zero, while the latter is an integer with the fundamental <matrix trace>. Hence the integral is defined modulo integers; integer-level exponentials are invariant under large <Yang-Mills gauge transformations>.
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