On the decomposition of global conformal invariants II

This paper is a continuation of [S. Alexakis, The decomposition of global conformal invariants 1, submitted for publication, see also math.DG/0509571], where we complete our partial proof of the Deser-Schwimmer conjecture on the structure of "global conformal invariants." Our theorem deals with such invariants P(g(n)) that locally depend only on the curvature tensor R-ijkl (without covariant derivatives). In [S. Alexakis, The decomposition of global conformal invariants I, Ann. of Math., in press] we developed a powerful tool, the "super divergence formula" which applies to any Riemannian operator that always integrates to zero on compact manifolds. In particular, it applies to the operator I(g)n (phi) that measures the "non-conformally invariant part" of P (g(n)). This paper resolves the problem of using this information we have obtained on the structure of I(g)n (phi) to understand the structure of P(g(n)). (C) 2005 Elsevier Inc. All rights reserved.