On pp.2 of Dijkgraaf and Witten's paper Topological gauge theories and group cohomology, the authors mentioned that the Chern-Simons action functional defined in equation (1.3) for 4-manifolds would be independent (modulo 1) of the choice of the 4-manifold $B$, and the extension of the principal $G$-bundle $E$ over the given 3-manifold $M = \partial{B}$ and its connection $A$ when $k$ is an integer. I wonder what "standard argument" the authors refer to.

On pp.3 there is also a "standard argument" showing that (1.5) is independent of the interpolating connection $A''$ for the 4-manifold $B = M \times I$ with boundary $\partial{B} = M \cup (-M)$.

Could somebody explain that?


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