The decomposition of Global Conformal Invariants V

This is the fifth in a series of papers where we prove a conjecture of Deser and Schwimmer regarding the algebraic structure of ``global conformal invariants''; these are defined to be conformally invariant integrals of geometric scalars. The conjecture asserts that the integrand of any such integral can be expressed as a linear combination of a local conformal invariant, a divergence and of the Chern-Gauss-Bonnet integrand. The present paper complements [6] in reducing the purely algebraic results that were used in [3,4 to certain simpler Lemmas, which will be proven in the last paper in this series, [8].