This paper complements our research
monograph The decomposition of global conformal invariants (Princeton University Press, 2012)
in proving 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 provides a proof of certain purely algebraic statements
announced in our previous work and whose rather technical proof was deferred to this
paper; the lemmas proven here serve to reduce “main algebraic propositions” to
certain technical inductive statements.
Keywords
conformal invariant, global conformal invariant,
Deser–Schwimmer conjecture, Riemannian invariant
