We conclude our analysis of bubble divergences in the flat spinfoam model. In
[arXiv:1008.1476] we showed that the divergence degree of an arbitrary
two-complex Gamma can be evaluated exactly by means of twisted cohomology.
Here, we specialize this result to the case where Gamma is the two-skeleton of
the cell decomposition of a pseudomanifold, and sharpen it with a careful
analysis of the cellular and topological structures involved. Moreover, we
explain in detail how this approach reproduces all the previous powercounting
results for the Boulatov-Ooguri (colored) tensor models, and sheds light on
algebraic-topological aspects of Gurau's 1/N expansion.Comment: 19 page