On the conformal properties of topological terms in even dimensions

Conformal properties of the topological gravitational terms in D = 2, D = 4 and D = 6 are discussed. It is shown that, in the last two cases, the integrands of these terms, when being settled into the dimension D - 1 and multiplied by a scalar, become conformal invariant. Furthermore we present a simple covariant derivation of the Paneitz operator in D = 4 and formulate two general conjectures concerning the conformal properties of topological structures in even dimensions.