  This paper forms part of a larger work 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.
