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It is shown that the addition of a topological invariant (Gauss-Bonnet term)to the anti-de Sitter (AdS) gravity action in four dimensions recovers thestandard regularization given by holographic renormalization procedure. Thiscrucial step makes possible the inclusion of an odd parity invariant(Pontryagin term) whose coupling is fixed by demanding an asymptotic (anti)self-dual condition on the Weyl tensor. This argument allows to find the dualpoint of the theory where the holographic stress tensor is related to theboundary Cotton tensor as $T_{j}^{i}=\pm (\ell ^{2}/8\pi G)C_{j}^{i}$, whichhas been observed in recent literature in solitonic solutions and hydrodynamicmodels.  A general procedure to generate the counterterm series for AdS gravity in anyeven dimension from the corresponding Euler term is also briefly discussed.

Topological regularization and self-duality in four-dimensional anti-de Sitter gravity