Remarks on 2+1 self-dual Chern-Simons gravity - art. no. 085022

We study 2 + 1 Chern-Simons gravity at the classical action level. In parti cular we rederive the linear combinations of the "standard" and "exotic" Ei nstein actions, from the (anti-)self-duality of the "internal" Lorentzian i ndices. The relation to a genuine four-dimensional (anti-)self-dual topolog ical theory greatly facilitates the analysis and its relation to hyperbolic three-dimensional geometry. Finally a non-Abelian vector field "dual" acti on is also obtained.