Bubble Divergences: Sorting out Topology from Cell Structure

Abstract

We conclude our analysis of bubble divergences in the flat spinfoam model. In Bonzom and Smerlak, Comm. Math. Phys., (submitted), we showed that the divergence degree of an arbitrary 2-complex Γ can be evaluated exactly by means of twisted cohomology. Here, we specialize this result to the case where Γ is the 2-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. © 2011 Springer Basel AG.