Manifold invariants affect dynamics in ADS gravity
  The first-order Holst action with negative cosmological constant is rendered finite by requiring functional differentiability on the configuration space of tetrads and connections. The surface terms that arise in the action for ADS gravity are equivalent to the Euler and Pontryagin densities with fixed weight factors; these terms modify the Noether charges that arise from diffeomorphism invariance of the action. 
Tomas Liko
gr-qc hep-th