  A positive semi-definite Euclidean action for arbitrary four-topologies can
be constructed by adding appropriate Yang-Mills and topological terms to the
Samuel-Jacobson-Smolin action of gravity with (anti)self-dual variables.
Moreover, on-shell, the (anti)self-dual sector of the new theory corresponds
precisely to all Einstein manifolds in four dimensions. The Lorentzian
signature action, and its analytic continuations are also considered. A
self-contained discussion is given on the effects of discrete transformations
C, P and T on the Samuel-Jacobson-Smolin action, and other proposed actions
which utilize self- or anti-self-dual variables as fundamental variables in the
description of four-dimensional gravity.
