  We compute the formal Poisson cohomology of a broken Lefschetz fibration by
calculating it at fold and Lefschetz singularities. Near a fold singularity the
computation reduces to that for a point singularity in 3 dimensions. For the
Poisson cohomology around singular points we adapt techniques developed for the
Sklyanin algebra. As a side result, we give compact formulas for the Poisson
coboundary operator of an arbitrary Jacobian Poisson structure in 4 dimensions.
