Ok, so I am still trying to make my way through the paper by Dijkgraaf and Witten "Group Cohomology and Topological Actions" (see http://citeseer.ist.psu.edu/viewdoc/download;jsessionid=807BE383780883ACB4CAB8BD48E8C90B?doi=10.1.1.128.1806&rep=rep1&type=pdf ), and I have a question (what's new). The authors start by showing how one can define the action over an arbitrary 3manifold $M$ as $n\cdot S = \frac{k}{8\pi^2}\int_B \langle F\wedge F\rangle$ $(mod\textrm{ }1)$. From here they say that they need to get rid of the $n$fold ambiguity in the definition of the action. So, to do this they add $\langle \gamma^*(\omega),B\rangle$ to the action, where $\gamma:B\rightarrow BG$, and $B$ is a 4manifold which has n copies of $M$ as its boundary. Does anyone know how they arrived at this being the correct term to add (cf. equation 3.4  3.5)? Thanks.
