Topological gravity and Chern–Simons forms in d = 4

Following the construction introduced by Antoniadis and Savvidy in Refs. [1], [2] and [3], we study metric-independent topological invariants on a (2n+1)(2n+1)-dimensional space–time. These invariants allow us to show that Chamseddine's even-dimensional topological gravity corresponds to a Chern–Simons–Antoniadis–Savvidy form. Starting from this result, more general four-dimensional topological gravity actions are explicitly constructed.